Solve the quadratic equation by completing the square. Verify your answer graphically. -x^2 + x -...

Question:

Solve the quadratic equation by completing the square. Verify your answer graphically.

{eq}-x^2 + x - 1 = 0 {/eq}

Completing the Square:

One of the most famous equations from high school algebra is the quadratic equation. Many students spend a lot of time trying to memorize this formula. But they don't have to. The quadratic equation is simply a generalization of what we end up with when we use the method of completing the square. In other words, we can always find a solution to a quadratic equation by completing the square. Completing the square takes advantage of the fact that {eq}(x+a)^2 = x^2 + 2ax +a^2 {/eq}. When we already have {eq}x^2 + 2ax {/eq} on one side of a quadratic equation, we can add {eq}a^2 {/eq} to both sides so that we have a perfect square.

Answer and Explanation: 1

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We're not big fans of having a negative sign in front of our leading term, so let's start by rewriting the equation by moving {eq}-x^2+x {/eq} over...

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Write the Standard Form of an Equation by Completing the Square

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Chapter 6 / Lesson 3
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What does completing the square mean? Learn about the formula for completing the square, and see how to rewrite the equation by completing the square.


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