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Simplifying 8x7 + -57x6 + 96x5 = 0 Reorder the terms: 96x5 + -57x6 + 8x7 = 0 Solving 96x5 + -57x6 + 8x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x5'. x5(96 + -57x + 8x2) = 0Subproblem 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 '(96 + -57x + 8x2)' equal to zero and attempt to solve: Simplifying 96 + -57x + 8x2 = 0 Solving 96 + -57x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 12 + -7.125x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -7.125x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -7.125x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -7.125x + x2 = 0 + -12 -7.125x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -7.125x + x2 = -12 The x term is -7.125x. Take half its coefficient (-3.5625). Square it (12.69140625) and add it to both sides. Add '12.69140625' to each side of the equation. -7.125x + 12.69140625 + x2 = -12 + 12.69140625 Reorder the terms: 12.69140625 + -7.125x + x2 = -12 + 12.69140625 Combine like terms: -12 + 12.69140625 = 0.69140625 12.69140625 + -7.125x + x2 = 0.69140625 Factor a perfect square on the left side: (x + -3.5625)(x + -3.5625) = 0.69140625 Calculate the square root of the right side: 0.831508418 Break this problem into two subproblems by setting (x + -3.5625) equal to 0.831508418 and -0.831508418.Subproblem 1
x + -3.5625 = 0.831508418 Simplifying x + -3.5625 = 0.831508418 Reorder the terms: -3.5625 + x = 0.831508418 Solving -3.5625 + x = 0.831508418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5625' to each side of the equation. -3.5625 + 3.5625 + x = 0.831508418 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + x = 0.831508418 + 3.5625 x = 0.831508418 + 3.5625 Combine like terms: 0.831508418 + 3.5625 = 4.394008418 x = 4.394008418 Simplifying x = 4.394008418Subproblem 2
x + -3.5625 = -0.831508418 Simplifying x + -3.5625 = -0.831508418 Reorder the terms: -3.5625 + x = -0.831508418 Solving -3.5625 + x = -0.831508418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5625' to each side of the equation. -3.5625 + 3.5625 + x = -0.831508418 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + x = -0.831508418 + 3.5625 x = -0.831508418 + 3.5625 Combine like terms: -0.831508418 + 3.5625 = 2.730991582 x = 2.730991582 Simplifying x = 2.730991582Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.394008418, 2.730991582}Solution
x = {4.394008418, 2.730991582}
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