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egoroff_w [7]
3 years ago
10

What equation results from completing the square and then factoring? x2 + 10X = 15

Mathematics
1 answer:
Mandarinka [93]3 years ago
3 0

Answer:

C) (x + 5)² = 40

Step-by-step explanation:

Given the quadratic equation, x² + 10x = 15:

To complete the square, take the coefficient of the middle term (b), and divide it by 2<em>a</em>:

x² + 10x + [\frac{b}{2a}]^{2}  = 15 + [\frac{b}{2a}]^{2}

x² + 10x + [\frac{10}{2}]^{2}  = 15 + [\frac{10}{2}]^{2}  

x² + 10x + 5²  = 15 + 5²

x² + 10x + 25 = 40

The trinomial on the left-hand side of the equation provides a perfect square binomial factors: <em>u</em>² + 2<em>uv</em> + v² = (<em>u</em> + <em>v</em>)²

x² + 10x + 25 = 40

(x + 5)²  = 40

Therefore, the correct answer is Option C)  (x + 5)²  = 40

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