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Simplifying -4x6 + -24x5 + 6x4 = 0 Reorder the terms: 6x4 + -24x5 + -4x6 = 0 Solving 6x4 + -24x5 + -4x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x4'. 2x4(3 + -12x + -2x2) = 0 Ignore the factor 2.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 '(3 + -12x + -2x2)' equal to zero and attempt to solve: Simplifying 3 + -12x + -2x2 = 0 Solving 3 + -12x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1.5 + 6x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 6x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 6x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 6x + x2 = 0 + 1.5 6x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 6x + x2 = 1.5 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 = 1.5 + 9 Reorder the terms: 9 + 6x + x2 = 1.5 + 9 Combine like terms: 1.5 + 9 = 10.5 9 + 6x + x2 = 10.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 10.5 Calculate the square root of the right side: 3.240370349 Break this problem into two subproblems by setting (x + 3) equal to 3.240370349 and -3.240370349.Subproblem 1
x + 3 = 3.240370349 Simplifying x + 3 = 3.240370349 Reorder the terms: 3 + x = 3.240370349 Solving 3 + x = 3.240370349 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 = 3.240370349 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.240370349 + -3 x = 3.240370349 + -3 Combine like terms: 3.240370349 + -3 = 0.240370349 x = 0.240370349 Simplifying x = 0.240370349Subproblem 2
x + 3 = -3.240370349 Simplifying x + 3 = -3.240370349 Reorder the terms: 3 + x = -3.240370349 Solving 3 + x = -3.240370349 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 = -3.240370349 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.240370349 + -3 x = -3.240370349 + -3 Combine like terms: -3.240370349 + -3 = -6.240370349 x = -6.240370349 Simplifying x = -6.240370349Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.240370349, -6.240370349}Solution
x = {0.240370349, -6.240370349}
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