Reviewed by Yaren Fadiloglulari
What is the only solution of 2x² + 8x = x² – 16?
Answer: The only solution of 2x² + 8x = x² – 16 is x = -16
This problem asks you to solve the quadratic equation 2x² + 8x = x² – 16. Solving quadratic equations typically involves moving all terms to one side, simplifying, and then factoring or applying the quadratic formula. Here, we'll find the unique value of x that satisfies the equation.
Methods
Math Tutor Explanation Using Rearrangement and Factoring
Move all terms to one side to form a standard quadratic equation and then factor to find the value of x.
Step 1: Step 1: Subtract x² – 16 from both sides to get 2x² + 8x – x² + 16 = 0
Step 2: Step 2: Combine like terms: x² + 8x + 16 = 0
Math Tutor Explanation Using the Quadratic Formula
Apply the quadratic formula x = [-b ± √(b²–4ac)] / 2a to the simplified equation to find the solution.
Step 1: Step 1: Recognize the equation as x² + 8x + 16 = 0, with a = 1, b = 8, c = 16
Step 2: Step 2: Plug into the quadratic formula: x = [-8 ± √(64 – 64)] / 2
Step 1:
Step 2:
Math Tutor suggests: More Practice with Quadratic Equations and Solutions
If you're working on solving quadratic equations, try these related questions to deepen your understanding.
FAQ on Solving Quadratic Equations
What is a quadratic equation?
A quadratic equation is an equation of the form ax² + bx + c = 0, where a ≠ 0.
How do you know if a quadratic equation has one or two solutions?
You can check the discriminant (b² – 4ac); if it's zero, there's one solution, and if it's positive, there are two real solutions.
What does it mean to factor a quadratic equation?
Factoring means expressing the quadratic as a product of two binomials set equal to zero.
What if a quadratic cannot be factored easily?
You can always use the quadratic formula or complete the square to find the solutions.
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