Question

Solve the equation. (x + 4)^2 = 15 - 2x^2. Quadratic Formula

Answer 1

The equation has two solutions $x_{1}$ =  [-4 + 2√13]/3] and

$x_{2}$ = [-4 - 2√13]/3]

Given the question:

(x + 4)^2 = 15 - 2x^2.

To solve the above Equation by using Quadratic Formula:
Solving Steps of Equation:

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

Expand the expression

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

Move the expression to the left

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

Collect like terms

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

Use the Quadratic formula:

x = [-b ± √(b2 – 4ac)]/2a

x = [-8 ± √(8^2 – 4x3x1)]/2x 3

Multiply and evaluate :

x = [-8± √(64 – 12)]/6]

Calculate:

x = [-8± 2√13]/6]

Separate the solutions

$x_{1}$ =  [-4 + 2√13]/3]

$x_{2}$ = [-4 - 2√13]/3]

Hence, The equation has two solutions $x_{1}$ =  [-4 + 2√13]/3] and

$x_{2}$ = [-4 - 2√13]/3]

Learn more about Quadratic Formula at:

brainly.com/question/9300679

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