Solve for x (x+4)^2=15-2x^2

${(x + 4)}^{2} = 15 - 2 x^{2}$

Move all terms containing $x$ to the left side of the equation.

Add $2 x^{2}$ to both sides of the equation.

${(x + 4)}^{2} + 2 x^{2} = 15$

Simplify each term.

Rewrite ${(x + 4)}^{2}$ as $(x + 4) (x + 4)$ .

$(x + 4) (x + 4) + 2 x^{2} = 15$

Expand $(x + 4) (x + 4)$ using the FOIL Method.

Apply the distributive property.

$x (x + 4) + 4 (x + 4) + 2 x^{2} = 15$

Apply the distributive property.

$x \cdot x + x \cdot 4 + 4 (x + 4) + 2 x^{2} = 15$

Apply the distributive property.

$x \cdot x + x \cdot 4 + 4 x + 4 \cdot 4 + 2 x^{2} = 15$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 4 + 4 x + 4 \cdot 4 + 2 x^{2} = 15$

Move $4$ to the left of $x$ .

$x^{2} + 4 \cdot x + 4 x + 4 \cdot 4 + 2 x^{2} = 15$

Multiply $4$ by $4$ .

$x^{2} + 4 x + 4 x + 16 + 2 x^{2} = 15$

Add $4 x$ and $4 x$ .

$x^{2} + 8 x + 16 + 2 x^{2} = 15$

Add $x^{2}$ and $2 x^{2}$ .

$3 x^{2} + 8 x + 16 = 15$

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

Subtract $15$ from both sides of the equation.

$3 x^{2} + 8 x + 16 - 15 = 0$

Subtract $15$ from $16$ .

$3 x^{2} + 8 x + 1 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 3$ , $b = 8$ , and $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{- 8 \pm \sqrt{8^{2} - 4 \cdot (3 \cdot 1)}}{2 \cdot 3}$

Simplify.

Simplify the numerator.

Raise $8$ to the power of $2$ .

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot 3 \cdot 1}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$x = \frac{- 8 \pm \sqrt{64 - 12 \cdot 1}}{2 \cdot 3}$

Multiply $- 12$ by $1$ .

$x = \frac{- 8 \pm \sqrt{64 - 12}}{2 \cdot 3}$

Subtract $12$ from $64$ .

$x = \frac{- 8 \pm \sqrt{52}}{2 \cdot 3}$

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$x = \frac{- 8 \pm \sqrt{4 (13)}}{2 \cdot 3}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 8 \pm \sqrt{2^{2} \cdot 13}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{- 8 \pm 2 \sqrt{13}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 8 \pm 2 \sqrt{13}}{6}$

Simplify $\frac{- 8 \pm 2 \sqrt{13}}{6}$ .

$x = \frac{- 4 \pm \sqrt{13}}{3}$

The final answer is the combination of both solutions.

$x = - \frac{4 - \sqrt{13}}{3}, - \frac{4 + \sqrt{13}}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4 - \sqrt{13}}{3}, - \frac{4 + \sqrt{13}}{3}$

Decimal Form:

$x = - 0.13148290 \dots, - 2.53518375 \dots$

Solve for x (x+4)^2=15-2x^2

Related Questions

Support LCMGCF.com by disabling your adblocker.