4x^2=-8(x^2-10x+25)

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Solution for 4x^2=-8(x^2-10x+25) equation:


Simplifying
4x2 = -8(x2 + -10x + 25)

Reorder the terms:
4x2 = -8(25 + -10x + x2)
4x2 = (25 * -8 + -10x * -8 + x2 * -8)
4x2 = (-200 + 80x + -8x2)

Solving
4x2 = -200 + 80x + -8x2

Solving for variable 'x'.

Reorder the terms:
200 + -80x + 4x2 + 8x2 = -200 + 80x + -8x2 + 200 + -80x + 8x2

Combine like terms: 4x2 + 8x2 = 12x2
200 + -80x + 12x2 = -200 + 80x + -8x2 + 200 + -80x + 8x2

Reorder the terms:
200 + -80x + 12x2 = -200 + 200 + 80x + -80x + -8x2 + 8x2

Combine like terms: -200 + 200 = 0
200 + -80x + 12x2 = 0 + 80x + -80x + -8x2 + 8x2
200 + -80x + 12x2 = 80x + -80x + -8x2 + 8x2

Combine like terms: 80x + -80x = 0
200 + -80x + 12x2 = 0 + -8x2 + 8x2
200 + -80x + 12x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
200 + -80x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(50 + -20x + 3x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(50 + -20x + 3x2)' equal to zero and attempt to solve: Simplifying 50 + -20x + 3x2 = 0 Solving 50 + -20x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 16.66666667 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '-16.66666667' to each side of the equation. 16.66666667 + -6.666666667x + -16.66666667 + x2 = 0 + -16.66666667 Reorder the terms: 16.66666667 + -16.66666667 + -6.666666667x + x2 = 0 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + -6.666666667x + x2 = 0 + -16.66666667 -6.666666667x + x2 = 0 + -16.66666667 Combine like terms: 0 + -16.66666667 = -16.66666667 -6.666666667x + x2 = -16.66666667 The x term is -6.666666667x. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667x + 11.11111112 + x2 = -16.66666667 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = -16.66666667 + 11.11111112 Combine like terms: -16.66666667 + 11.11111112 = -5.55555555 11.11111112 + -6.666666667x + x2 = -5.55555555 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = -5.55555555 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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