Reviewed by Camille Ira B. Mendoza
What is the only solution of 2x² + 8x = x² - 16?
Answer: The only solution of 2x² + 8x = x² - 16 is x = -4.
Solving quadratic equations is a fundamental skill in algebra that involves finding values of x that satisfy the equation. This equation requires combining like terms and factoring to find the solution. Quadratic equations appear in many real-world applications including physics, engineering, and economics.
Methods
Math Tutor Explanation Using the Factoring Method
Factoring works because a perfect square trinomial can be written as a squared binomial.
Step 1: Rearrange the equation by moving all terms to one side: 2x² + 8x - x² + 16 = 0, which simplifies to x² + 8x + 16 = 0.
Step 2: Factor the perfect square trinomial (x + 4)² = 0, giving x = -4 as the only solution.
Math Tutor Explanation Using the Quadratic Formula Method
The quadratic formula provides a direct way to find solutions for any quadratic equation.
Step 1: Rewrite the equation in standard form x² + 8x + 16 = 0 and identify a = 1, b = 8, c = 16.
Step 2: Apply the formula x = (-8 ± √(64 - 64)) / 2 = -8/2 = -4.
Step 1:
Step 2:
Math Tutor suggests: Practice Solving Quadratic Equations
Try these related quadratic equation problems to strengthen your factoring and solving skills.
FAQ on Quadratic Equations
What is a quadratic equation?
A quadratic equation is a polynomial equation of degree 2, written in the form ax² + bx + c = 0.
What is a perfect square trinomial?
A perfect square trinomial is a trinomial that can be factored into the square of a binomial.
When does a quadratic equation have only one solution?
A quadratic has one solution when the discriminant (b² - 4ac) equals zero.
What is the discriminant?
The discriminant is b² - 4ac and determines the number of real solutions a quadratic equation has.
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