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.

x = (√11 + 5) / 2, and x = ( - √11 + 5) / 2

Step-by-step explanation:

Let us solve by completing the square;

7 = - 2x^2 + 10x, ⇒ Switch sides,

- 2x^2 + 10x = 7, ⇒ Divide both sides by - 2,

x^2 - 5x = - 7 / 2, ⇒ Write the equation in the form x^2 + 2ax + a^2, (x + a) ^2, solving for the value of a,

2ax = - 5x,

a = - 5x / 2x,

a = - 5 / 2, ⇒ Add a^2 ⇒ ( - 5 / 2) ^2 to either side of equation,

x^2 - 5x + ( - 5 / 2) ^2 = - 7 / 2 + ( - 5 / 2) ^2, ⇒ Simplify,

(x - 5 / 2) ^2 = 11 / 4,

| x - 5 / 2 | = √ (11 / 4), Solve for value (s) of x,

Answer; x = (√11 + 5) / 2, and x = ( - √11 + 5) / 2