108=16x^2-22x+220

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Solution for 108=16x^2-22x+220 equation:


Simplifying
108 = 16x2 + -22x + 220

Reorder the terms:
108 = 220 + -22x + 16x2

Solving
108 = 220 + -22x + 16x2

Solving for variable 'x'.

Combine like terms: 108 + -220 = -112
-112 + 22x + -16x2 = 220 + -22x + 16x2 + -220 + 22x + -16x2

Reorder the terms:
-112 + 22x + -16x2 = 220 + -220 + -22x + 22x + 16x2 + -16x2

Combine like terms: 220 + -220 = 0
-112 + 22x + -16x2 = 0 + -22x + 22x + 16x2 + -16x2
-112 + 22x + -16x2 = -22x + 22x + 16x2 + -16x2

Combine like terms: -22x + 22x = 0
-112 + 22x + -16x2 = 0 + 16x2 + -16x2
-112 + 22x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-112 + 22x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-56 + 11x + -8x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-56 + 11x + -8x2)' equal to zero and attempt to solve: Simplifying -56 + 11x + -8x2 = 0 Solving -56 + 11x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 7 + -1.375x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -1.375x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -1.375x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1.375x + x2 = 0 + -7 -1.375x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -1.375x + x2 = -7 The x term is -1.375x. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375x + 0.47265625 + x2 = -7 + 0.47265625 Reorder the terms: 0.47265625 + -1.375x + x2 = -7 + 0.47265625 Combine like terms: -7 + 0.47265625 = -6.52734375 0.47265625 + -1.375x + x2 = -6.52734375 Factor a perfect square on the left side: (x + -0.6875)(x + -0.6875) = -6.52734375 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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