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Simplifying -6(x + -3) + -7(2x + -8)(2x + -7) = 0 Reorder the terms: -6(-3 + x) + -7(2x + -8)(2x + -7) = 0 (-3 * -6 + x * -6) + -7(2x + -8)(2x + -7) = 0 (18 + -6x) + -7(2x + -8)(2x + -7) = 0 Reorder the terms: 18 + -6x + -7(-8 + 2x)(2x + -7) = 0 Reorder the terms: 18 + -6x + -7(-8 + 2x)(-7 + 2x) = 0 Multiply (-8 + 2x) * (-7 + 2x) 18 + -6x + -7(-8(-7 + 2x) + 2x * (-7 + 2x)) = 0 18 + -6x + -7((-7 * -8 + 2x * -8) + 2x * (-7 + 2x)) = 0 18 + -6x + -7((56 + -16x) + 2x * (-7 + 2x)) = 0 18 + -6x + -7(56 + -16x + (-7 * 2x + 2x * 2x)) = 0 18 + -6x + -7(56 + -16x + (-14x + 4x2)) = 0 Combine like terms: -16x + -14x = -30x 18 + -6x + -7(56 + -30x + 4x2) = 0 18 + -6x + (56 * -7 + -30x * -7 + 4x2 * -7) = 0 18 + -6x + (-392 + 210x + -28x2) = 0 Reorder the terms: 18 + -392 + -6x + 210x + -28x2 = 0 Combine like terms: 18 + -392 = -374 -374 + -6x + 210x + -28x2 = 0 Combine like terms: -6x + 210x = 204x -374 + 204x + -28x2 = 0 Solving -374 + 204x + -28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-187 + 102x + -14x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-187 + 102x + -14x2)' equal to zero and attempt to solve: Simplifying -187 + 102x + -14x2 = 0 Solving -187 + 102x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. 13.35714286 + -7.285714286x + x2 = 0 Move the constant term to the right: Add '-13.35714286' to each side of the equation. 13.35714286 + -7.285714286x + -13.35714286 + x2 = 0 + -13.35714286 Reorder the terms: 13.35714286 + -13.35714286 + -7.285714286x + x2 = 0 + -13.35714286 Combine like terms: 13.35714286 + -13.35714286 = 0.00000000 0.00000000 + -7.285714286x + x2 = 0 + -13.35714286 -7.285714286x + x2 = 0 + -13.35714286 Combine like terms: 0 + -13.35714286 = -13.35714286 -7.285714286x + x2 = -13.35714286 The x term is -7.285714286x. Take half its coefficient (-3.642857143). Square it (13.27040816) and add it to both sides. Add '13.27040816' to each side of the equation. -7.285714286x + 13.27040816 + x2 = -13.35714286 + 13.27040816 Reorder the terms: 13.27040816 + -7.285714286x + x2 = -13.35714286 + 13.27040816 Combine like terms: -13.35714286 + 13.27040816 = -0.0867347 13.27040816 + -7.285714286x + x2 = -0.0867347 Factor a perfect square on the left side: (x + -3.642857143)(x + -3.642857143) = -0.0867347 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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