The solution to the quadratic expression 2x² + 8x = x² - 16 is x = -4
What is a quadratic expression?
A quadratic expression is an expression whose variable has the highest power of 2
The following is the step to determine the solution:
The equation is given as:
2x² + 8x = x² - 16
Collect like terms
2x² - x² + 8x + 16 = 0
Evaluate
x² + 8x + 16 = 0
Expand
x² + 4x + 4x + 16 = 0
Factorize
x(x + 4) + 4(x + 4) = 0
Factor out x + 4
(x + 4)(x + 4) = 0
Rewrite as:
(x + 4)² = 0
Take the square root of both sides
x + 4 = 0
Subtract 4 from both ides
x = -4
Hence, the solution to 2x² + 8x = x² - 16 is x = -4
Read more about quadratic expressions at:
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