Algebra Examples

$- a = b - \sqrt{x}$

Step 1

Rewrite the equation as $b - \sqrt{x} = - a$ .

$b - \sqrt{x} = - a$

Step 2

Subtract $b$ from both sides of the equation.

$- \sqrt{x} = - a - b$

Step 3

To remove the radical on the left side of the equation, square both sides of the equation.

${(- \sqrt{x})}^{2} = {(- a - b)}^{2}$

Step 4

Simplify each side of the equation.

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(- x^{\frac{1}{2}})}^{2} = {(- a - b)}^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${(- x^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1

Apply the product rule to $- x^{\frac{1}{2}}$ .

${(- 1)}^{2} {(x^{\frac{1}{2}})}^{2} = {(- a - b)}^{2}$

Step 4.2.1.2

Raise $- 1$ to the power of $2$ .

$1 {(x^{\frac{1}{2}})}^{2} = {(- a - b)}^{2}$

Step 4.2.1.3

Multiply ${(x^{\frac{1}{2}})}^{2}$ by $1$ .

${(x^{\frac{1}{2}})}^{2} = {(- a - b)}^{2}$

Step 4.2.1.4

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = {(- a - b)}^{2}$

Step 4.2.1.4.2

Cancel the common factor of $2$ .

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Step 4.2.1.4.2.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = {(- a - b)}^{2}$

Step 4.2.1.4.2.2

Rewrite the expression.

$x^{1} = {(- a - b)}^{2}$

Step 4.2.1.5

Simplify.

$x = {(- a - b)}^{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify ${(- a - b)}^{2}$ .

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Step 4.3.1.1

Rewrite ${(- a - b)}^{2}$ as $(- a - b) (- a - b)$ .

$x = (- a - b) (- a - b)$

Step 4.3.1.2

Expand $(- a - b) (- a - b)$ using the FOIL Method.

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Step 4.3.1.2.1

Apply the distributive property.

$x = - a (- a - b) - b (- a - b)$

Step 4.3.1.2.2

Apply the distributive property.

$x = - a (- a) - a (- b) - b (- a - b)$

Step 4.3.1.2.3

Apply the distributive property.

$x = - a (- a) - a (- b) - b (- a) - b (- b)$

Step 4.3.1.3

Simplify and combine like terms.

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Step 4.3.1.3.1

Simplify each term.

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Step 4.3.1.3.1.1

Rewrite using the commutative property of multiplication.

$x = - 1 \cdot - 1 a \cdot a - a (- b) - b (- a) - b (- b)$

Step 4.3.1.3.1.2

Multiply $a$ by $a$ by adding the exponents.

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Step 4.3.1.3.1.2.1

Move $a$ .

$x = - 1 \cdot - 1 (a \cdot a) - a (- b) - b (- a) - b (- b)$

Step 4.3.1.3.1.2.2

Multiply $a$ by $a$ .

$x = - 1 \cdot - 1 a^{2} - a (- b) - b (- a) - b (- b)$

Step 4.3.1.3.1.3

Multiply $- 1$ by $- 1$ .

$x = 1 a^{2} - a (- b) - b (- a) - b (- b)$

Step 4.3.1.3.1.4

Multiply $a^{2}$ by $1$ .

$x = a^{2} - a (- b) - b (- a) - b (- b)$

Step 4.3.1.3.1.5

Rewrite using the commutative property of multiplication.

$x = a^{2} - 1 \cdot - 1 a b - b (- a) - b (- b)$

Step 4.3.1.3.1.6

Multiply $- 1$ by $- 1$ .

$x = a^{2} + 1 a b - b (- a) - b (- b)$

Step 4.3.1.3.1.7

Multiply $a$ by $1$ .

$x = a^{2} + a b - b (- a) - b (- b)$

Step 4.3.1.3.1.8

Rewrite using the commutative property of multiplication.

$x = a^{2} + a b - 1 \cdot - 1 b a - b (- b)$

Step 4.3.1.3.1.9

Multiply $- 1$ by $- 1$ .

$x = a^{2} + a b + 1 b a - b (- b)$

Step 4.3.1.3.1.10

Multiply $b$ by $1$ .

$x = a^{2} + a b + b a - b (- b)$

Step 4.3.1.3.1.11

Rewrite using the commutative property of multiplication.

$x = a^{2} + a b + b a - 1 \cdot - 1 b \cdot b$

Step 4.3.1.3.1.12

Multiply $b$ by $b$ by adding the exponents.

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Step 4.3.1.3.1.12.1

Move $b$ .

$x = a^{2} + a b + b a - 1 \cdot - 1 (b \cdot b)$

Step 4.3.1.3.1.12.2

Multiply $b$ by $b$ .

$x = a^{2} + a b + b a - 1 \cdot - 1 b^{2}$

Step 4.3.1.3.1.13

Multiply $- 1$ by $- 1$ .

$x = a^{2} + a b + b a + 1 b^{2}$

Step 4.3.1.3.1.14

Multiply $b^{2}$ by $1$ .

$x = a^{2} + a b + b a + b^{2}$

Step 4.3.1.3.2

Add $a b$ and $b a$ .

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Step 4.3.1.3.2.1

Reorder $b$ and $a$ .

$x = a^{2} + a b + a b + b^{2}$

Step 4.3.1.3.2.2

Add $a b$ and $a b$ .

$x = a^{2} + 2 a b + b^{2}$