Solve Using the Quadratic Formula (x+7)(x-7)=-3x

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

Step 1

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

Simplify the left side.

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify terms.

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

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

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

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

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

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

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

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $7$ by $- 7$ .

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

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.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $- 49$ .

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

Add $9$ and $196$ .

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

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:

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

Solve Using the Quadratic Formula (x+7)(x-7)=-3x

Related Questions

Support LCMGCF.com by disabling your adblocker.