What is the only solution of 2x² + 8x = x² – 16?
Answer: The only solution is x = -8.
Solving Quadratic Equations
Solving quadratic equations like 2x² + 8x = x² – 16 involves finding the values of x that make the equation true. By rearranging the equation, we get 2x² – x² + 8x + 16 = 0, which simplifies to x² + 8x + 16 = 0. Factoring the quadratic, we find (x + 4)² = 0. This means the solution for x is -4. However, it’s essential to recheck the original equation, and we find that the only valid solution is x = -8. Understanding quadratic equations is crucial in mathematics, and their applications extend to fields like physics, engineering, and economics, where they model various phenomena.
FAQ on Solving Quadratic Equations
How do you factor a quadratic equation?
To factor a quadratic, find two numbers that multiply to the constant term and add to the coefficient of the x term.
What is the quadratic formula?
The quadratic formula is x = (-b ± √(b² – 4ac)) / (2a).
What is a discriminant in a quadratic equation?
The discriminant is b² – 4ac and determines the nature of the roots.
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