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Simplifying -6x5(-8x2 + 9x + 7) = 0 Reorder the terms: -6x5(7 + 9x + -8x2) = 0 (7 * -6x5 + 9x * -6x5 + -8x2 * -6x5) = 0 (-42x5 + -54x6 + 48x7) = 0 Solving -42x5 + -54x6 + 48x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x5'. 6x5(-7 + -9x + 8x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'x5' equal to zero and attempt to solve: Simplifying x5 = 0 Solving x5 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-7 + -9x + 8x2)' equal to zero and attempt to solve: Simplifying -7 + -9x + 8x2 = 0 Solving -7 + -9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -1.125x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -1.125x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -1.125x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -1.125x + x2 = 0 + 0.875 -1.125x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -1.125x + x2 = 0.875 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = 0.875 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 0.875 + 0.31640625 Combine like terms: 0.875 + 0.31640625 = 1.19140625 0.31640625 + -1.125x + x2 = 1.19140625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 1.19140625 Calculate the square root of the right side: 1.091515575 Break this problem into two subproblems by setting (x + -0.5625) equal to 1.091515575 and -1.091515575.Subproblem 1
x + -0.5625 = 1.091515575 Simplifying x + -0.5625 = 1.091515575 Reorder the terms: -0.5625 + x = 1.091515575 Solving -0.5625 + x = 1.091515575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 1.091515575 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 1.091515575 + 0.5625 x = 1.091515575 + 0.5625 Combine like terms: 1.091515575 + 0.5625 = 1.654015575 x = 1.654015575 Simplifying x = 1.654015575Subproblem 2
x + -0.5625 = -1.091515575 Simplifying x + -0.5625 = -1.091515575 Reorder the terms: -0.5625 + x = -1.091515575 Solving -0.5625 + x = -1.091515575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -1.091515575 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -1.091515575 + 0.5625 x = -1.091515575 + 0.5625 Combine like terms: -1.091515575 + 0.5625 = -0.529015575 x = -0.529015575 Simplifying x = -0.529015575Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.654015575, -0.529015575}Solution
x = {1.654015575, -0.529015575}
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