what is the only solution of $2x^2 + 8x = x^2 - 16$?
what is the only solution of $2x^2 + 8x = x^2 - 16$?
Answer
Explanation:
Step1: Simplify the equation
Subtract (x^2) and add 16 to both sides of the equation (2x^2 + 8x = x^2 - 16) to get a quadratic equation in standard form. (2x^2 - x^2 + 8x + 16 = 0) (x^2 + 8x + 16 = 0)
Step2: Factor the quadratic equation
Notice that (x^2 + 8x + 16) is a perfect square trinomial, which can be factored as ((x + 4)^2 = 0)
Step3: Solve for (x)
Set the factor equal to zero: (x + 4 = 0) Subtract 4 from both sides: (x = -4)
Answer:
(-4)