Algebra Examples

$18 - 3 y^{\frac{1}{2}} = 25$

Step 1

Subtract $25$ from both sides of the equation.

$18 - 3 y^{\frac{1}{2}} - 25 = 0$

Step 2

Subtract $25$ from $18$ .

$- 3 y^{\frac{1}{2}} - 7 = 0$

Step 3

Factor $- 1$ out of $- 3 y^{\frac{1}{2}} - 7$ .

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Step 3.1

Factor $- 1$ out of $- 3 y^{\frac{1}{2}}$ .

$- (3 y^{\frac{1}{2}}) - 7 = 0$

Step 3.2

Rewrite $- 7$ as $- 1 (7)$ .

$- (3 y^{\frac{1}{2}}) - 1 \cdot 7 = 0$

Step 3.3

Factor $- 1$ out of $- (3 y^{\frac{1}{2}}) - 1 (7)$ .

$- (3 y^{\frac{1}{2}} + 7) = 0$

Step 4

Simplify $- (3 y^{\frac{1}{2}} + 7)$ .

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Step 4.1

Apply the distributive property.

$- (3 y^{\frac{1}{2}}) - 1 \cdot 7 = 0$

Step 4.2

Multiply.

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Step 4.2.1

Multiply $3$ by $- 1$ .

$- 3 y^{\frac{1}{2}} - 1 \cdot 7 = 0$

Step 4.2.2

Multiply $- 1$ by $7$ .

$- 3 y^{\frac{1}{2}} - 7 = 0$

Step 5

Add $7$ to both sides of the equation.

$- 3 y^{\frac{1}{2}} = 7$

Step 6

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(- 3 y^{\frac{1}{2}})}^{2} = 7^{2}$

Step 7

Simplify the exponent.

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Step 7.1

Simplify the left side.

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Step 7.1.1

Simplify ${(- 3 y^{\frac{1}{2}})}^{2}$ .

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Step 7.1.1.1

Apply the product rule to $- 3 y^{\frac{1}{2}}$ .

${(- 3)}^{2} {(y^{\frac{1}{2}})}^{2} = 7^{2}$

Step 7.1.1.2

Raise $- 3$ to the power of $2$ .

$9 {(y^{\frac{1}{2}})}^{2} = 7^{2}$

Step 7.1.1.3

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

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Step 7.1.1.3.1

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

$9 y^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 7.1.1.3.2

Cancel the common factor of $2$ .

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Step 7.1.1.3.2.1

Cancel the common factor.

$9 y^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 7.1.1.3.2.2

Rewrite the expression.

$9 y^{1} = 7^{2}$

Step 7.1.1.4

Simplify.

$9 y = 7^{2}$

Step 7.2

Simplify the right side.

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Step 7.2.1

Raise $7$ to the power of $2$ .

$9 y = 49$

Step 8

Divide each term in $9 y = 49$ by $9$ and simplify.

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Step 8.1

Divide each term in $9 y = 49$ by $9$ .

$\frac{9 y}{9} = \frac{49}{9}$

Step 8.2

Simplify the left side.

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Step 8.2.1

Cancel the common factor of $9$ .

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Step 8.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{49}{9}$

Step 8.2.1.2

Divide $y$ by $1$ .

$y = \frac{49}{9}$

Step 9

Exclude the solutions that do not make $- (3 y^{\frac{1}{2}} + 7) = 0$ true.

$No solution$