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Novay_Z [31]
3 years ago
14

Determine the next step for solving the quadratic equation by completing the square.

Mathematics
1 answer:
Studentka2010 [4]3 years ago
4 0

Answer:

The solutions are x=\frac{1+\sqrt{7}}{2} and x=\frac{1-\sqrt{7}}{2}

Step-by-step explanation:

we have

0=-2x^{2}+2x+3

Group terms that contain the same variable, and move the constant to the opposite side of the equation

-3=-2x^{2}+2x

Factor the leading coefficient

-3=-2(x^{2}-x)

Complete the square. Remember to balance the equation by adding the same constants to each side.

-3-0.5=-2(x^{2}-x+0.5^{2})

-3.5=-2(x^{2}-x+0.5^{2})

Rewrite as perfect squares

-3.5=-2(x-0.5)^{2}

7/4=(x-0.5)^{2}

square root both sides

x-0.5=(+/-)\sqrt{\frac{7}{4}}

x-\frac{1}{2}=(+/-)\frac{\sqrt{7}}{2}

x=\frac{1}{2}(+/-)\frac{\sqrt{7}}{2}

x=\frac{1+\sqrt{7}}{2}

x=\frac{1-\sqrt{7}}{2}

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