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Simplifying x7 = 6x6 + x5 Reorder the terms: x7 = x5 + 6x6 Solving x7 = x5 + 6x6 Solving for variable 'x'. Reorder the terms: -1x5 + -6x6 + x7 = x5 + 6x6 + -1x5 + -6x6 Reorder the terms: -1x5 + -6x6 + x7 = x5 + -1x5 + 6x6 + -6x6 Combine like terms: x5 + -1x5 = 0 -1x5 + -6x6 + x7 = 0 + 6x6 + -6x6 -1x5 + -6x6 + x7 = 6x6 + -6x6 Combine like terms: 6x6 + -6x6 = 0 -1x5 + -6x6 + x7 = 0 Factor out the Greatest Common Factor (GCF), 'x5'. x5(-1 + -6x + x2) = 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 '(-1 + -6x + x2)' equal to zero and attempt to solve: Simplifying -1 + -6x + x2 = 0 Solving -1 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -6x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -6x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6x + x2 = 0 + 1 -6x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6x + x2 = 1 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 1 + 9 Reorder the terms: 9 + -6x + x2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + -6x + x2 = 10 Factor a perfect square on the left side: (x + -3)(x + -3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -3) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -3 = 3.16227766 Simplifying x + -3 = 3.16227766 Reorder the terms: -3 + x = 3.16227766 Solving -3 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.16227766 + 3 x = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 x = 6.16227766 Simplifying x = 6.16227766Subproblem 2
x + -3 = -3.16227766 Simplifying x + -3 = -3.16227766 Reorder the terms: -3 + x = -3.16227766 Solving -3 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.16227766 + 3 x = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 x = -0.16227766 Simplifying x = -0.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.16227766, -0.16227766}Solution
x = {6.16227766, -0.16227766}
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