x*x+7x-8x*x-10x+20-2x=21

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Solution for x*x+7x-8x*x-10x+20-2x=21 equation:


Simplifying
x * x + 7x + -8x * x + -10x + 20 + -2x = 21

Multiply x * x
x2 + 7x + -8x * x + -10x + 20 + -2x = 21

Multiply x * x
x2 + 7x + -8x2 + -10x + 20 + -2x = 21

Reorder the terms:
20 + 7x + -10x + -2x + x2 + -8x2 = 21

Combine like terms: 7x + -10x = -3x
20 + -3x + -2x + x2 + -8x2 = 21

Combine like terms: -3x + -2x = -5x
20 + -5x + x2 + -8x2 = 21

Combine like terms: x2 + -8x2 = -7x2
20 + -5x + -7x2 = 21

Solving
20 + -5x + -7x2 = 21

Solving for variable 'x'.

Reorder the terms:
20 + -21 + -5x + -7x2 = 21 + -21

Combine like terms: 20 + -21 = -1
-1 + -5x + -7x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-1 + -5x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 5x + 7x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(1 + 5x + 7x2)' equal to zero and attempt to solve: Simplifying 1 + 5x + 7x2 = 0 Solving 1 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.7142857143x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.7142857143x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.7142857143x + x2 = 0 + -0.1428571429 0.7142857143x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.7142857143x + x2 = -0.1428571429 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = -0.1428571429 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = -0.1428571429 + 0.1275510204 Combine like terms: -0.1428571429 + 0.1275510204 = -0.0153061225 0.1275510204 + 0.7142857143x + x2 = -0.0153061225 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = -0.0153061225 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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