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

0 = - 2x2 + 2x + 3

-3 = - 2x2 + 2x

-3 = - 2 (x2 - x)

-3 + = - 2 (x2 - x + )

StartFraction negative 7 Over 2 EndFraction = - 2 (x - StartFraction 1 Over 2 EndFraction) 2

StartFraction 7 Over 4 EndFraction = (x - StartFraction 1 Over 2 EndFraction) 2

The two solutions are Plus or minus StartFraction StartRoot 7 EndRoot Over 2 EndFraction

Question

Clay Dillon

Mathematics

17 June, 06:33

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

0 = - 2x2 + 2x + 3

-3 = - 2x2 + 2x

-3 = - 2 (x2 - x)

-3 + = - 2 (x2 - x + )

StartFraction negative 7 Over 2 EndFraction = - 2 (x - StartFraction 1 Over 2 EndFraction) 2

StartFraction 7 Over 4 EndFraction = (x - StartFraction 1 Over 2 EndFraction) 2

The two solutions are Plus or minus StartFraction StartRoot 7 EndRoot Over 2 EndFraction

+1

Answers (2)

Know the Answer?

Heather Hayden · Answer 1

A) StartFraction negative 7 Over 2 EndFraction = - 2 (x - StartFraction 1 Over 2 EndFraction) 2

Step-by-step explanation:

-3 + = - 2 (x² - x + )

-3 + - 2 (½) ² = - 2 (x² - 2 (x) (½) + (½) ²)

-3 - ½ = - 2 (x - ½) ²

-7/2 = - 2 (x - ½) ²

Amina Lynch · Answer 2

-7/2 = - 2 (x-1/2) ^2

Step-by-step explanation:

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

Subtract 3 from each side

-3 = - 2x^2 + 2x

Factor out the - 2

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

Take the coefficient of x and divide by 2 and square it

-1 / 2 = - 1/2 ^2 = 1/4

Add it to each side Remember the - 2 on the outside so we need to multiply it by - 2

-2 * 1/4 = - 1/2

-3 - 1/2 = - 2 (x^2 - x + 1/4)

-7/2 = - 2 (x^2 - x + 1/4)

-7/2 = - 2 (x-1/2) ^2