Question

Complete the steps for solving 7 = –2x2 + 10x. Factor out of the variable terms. inside the parentheses and on the left side of the equation. Write the perfect square trinomial as a binomial squared. Divide both sides by –2. Use the square root property of equality. Add to both sides

Answer 1

we have

$7=-2x^{2} +10x$

Factor the leading coefficient

$7=-2(x^{2} -5x)$

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

$7-12.50=-2(x^{2} -5x+2.5^{2})$

$-5.50=-2(x^{2} -5x+2.5^{2})$

Divide both sides by $-2$

$2.75=(x^{2} -5x+2.5^{2})$

Rewrite as perfect squares

$2.75=(x-2.5)^{2}$

Taking the square roots of both sides (square root property of equality)

$x-2.5=(+/-)\sqrt{2.75}$

Remember that

$\sqrt{2.75}=\sqrt{\frac{11}{4}}= \frac{\sqrt{11}}{2}$

$x-2.5=(+/-)\frac{\sqrt{11}}{2}$

$x=2.5(+/-)\frac{\sqrt{11}}{2}$

$x=2.5+\frac{\sqrt{11}}{2}=\frac{5+\sqrt{11}}{2}$

$x=2.5-\frac{\sqrt{11}}{2}=\frac{5-\sqrt{11}}{2}$

the answer is

The solutions are

$x=\frac{5+\sqrt{11}}{2}$

$x=\frac{5-\sqrt{11}}{2}$

Answer 2

Answer:

1) -2, 2) Add 25/4 and subtract 25/2 6) 5/2

Step-by-step explanation:

did it on edgenunity :)