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Simplifying 7x6 + -56x5 + 42x4 = 0 Reorder the terms: 42x4 + -56x5 + 7x6 = 0 Solving 42x4 + -56x5 + 7x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7x4'. 7x4(6 + -8x + x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 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 '(6 + -8x + x2)' equal to zero and attempt to solve: Simplifying 6 + -8x + x2 = 0 Solving 6 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -8x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -8x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -8x + x2 = 0 + -6 -8x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -8x + x2 = -6 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -6 + 16 Reorder the terms: 16 + -8x + x2 = -6 + 16 Combine like terms: -6 + 16 = 10 16 + -8x + x2 = 10 Factor a perfect square on the left side: (x + -4)(x + -4) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -4) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -4 = 3.16227766 Simplifying x + -4 = 3.16227766 Reorder the terms: -4 + x = 3.16227766 Solving -4 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.16227766 + 4 x = 3.16227766 + 4 Combine like terms: 3.16227766 + 4 = 7.16227766 x = 7.16227766 Simplifying x = 7.16227766Subproblem 2
x + -4 = -3.16227766 Simplifying x + -4 = -3.16227766 Reorder the terms: -4 + x = -3.16227766 Solving -4 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.16227766 + 4 x = -3.16227766 + 4 Combine like terms: -3.16227766 + 4 = 0.83772234 x = 0.83772234 Simplifying x = 0.83772234Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.16227766, 0.83772234}Solution
x = {7.16227766, 0.83772234}
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