Algebra Examples

$(x + 7) (x - 7) = - 3 x$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $(x + 7) (x - 7)$ .

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Step 1.1.1.1

Expand $(x + 7) (x - 7)$ using the FOIL Method.

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Step 1.1.1.1.1

Apply the distributive property.

$x (x - 7) + 7 (x - 7) = - 3 x$

Step 1.1.1.1.2

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 7 (x - 7) = - 3 x$

Step 1.1.1.1.3

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 7 x + 7 \cdot - 7 = - 3 x$

Step 1.1.1.2

Simplify terms.

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Step 1.1.1.2.1

Combine the opposite terms in $x \cdot x + x \cdot - 7 + 7 x + 7 \cdot - 7$ .

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Step 1.1.1.2.1.1

Reorder the factors in the terms $x \cdot - 7$ and $7 x$ .

$x \cdot x - 7 x + 7 x + 7 \cdot - 7 = - 3 x$

Step 1.1.1.2.1.2

Add $- 7 x$ and $7 x$ .

$x \cdot x + 0 + 7 \cdot - 7 = - 3 x$

Step 1.1.1.2.1.3

Add $x \cdot x$ and $0$ .

$x \cdot x + 7 \cdot - 7 = - 3 x$

Step 1.1.1.2.2

Simplify each term.

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Step 1.1.1.2.2.1

Multiply $x$ by $x$ .

$x^{2} + 7 \cdot - 7 = - 3 x$

Step 1.1.1.2.2.2

Multiply $7$ by $- 7$ .

$x^{2} - 49 = - 3 x$

Step 1.2

Add $3 x$ to both sides of the equation.

$x^{2} - 49 + 3 x = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 3$ , and $c = - 49$ into the quadratic formula and solve for $x$ .

$\frac{- 3 \pm \sqrt{3^{2} - 4 \cdot (1 \cdot - 49)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot 1 \cdot - 49}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 49$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot - 49}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 49$ .

$x = \frac{- 3 \pm \sqrt{9 + 196}}{2 \cdot 1}$

Step 4.1.3

Add $9$ and $196$ .

$x = \frac{- 3 \pm \sqrt{205}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{- 3 \pm \sqrt{205}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 3 \pm \sqrt{205}}{2}$

Decimal Form:

$x = 5.65891053 \dots, - 8.65891053 \dots$