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MathematicsMathematics
2 May, 21:18

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

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Answers (2)
  1. 2 May, 21:39
    0
    -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
  2. 3 May, 00:54
    0
    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
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Home » Mathematics » 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 =
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