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Simplifying 135x + 106x2 + -1x3 = 0 Solving 135x + 106x2 + -1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(135 + 106x + -1x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(135 + 106x + -1x2)' equal to zero and attempt to solve: Simplifying 135 + 106x + -1x2 = 0 Solving 135 + 106x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -135 + -106x + x2 = 0 Move the constant term to the right: Add '135' to each side of the equation. -135 + -106x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + -106x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + -106x + x2 = 0 + 135 -106x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 -106x + x2 = 135 The x term is -106x. Take half its coefficient (-53). Square it (2809) and add it to both sides. Add '2809' to each side of the equation. -106x + 2809 + x2 = 135 + 2809 Reorder the terms: 2809 + -106x + x2 = 135 + 2809 Combine like terms: 135 + 2809 = 2944 2809 + -106x + x2 = 2944 Factor a perfect square on the left side: (x + -53)(x + -53) = 2944 Calculate the square root of the right side: 54.258639865 Break this problem into two subproblems by setting (x + -53) equal to 54.258639865 and -54.258639865.Subproblem 1
x + -53 = 54.258639865 Simplifying x + -53 = 54.258639865 Reorder the terms: -53 + x = 54.258639865 Solving -53 + x = 54.258639865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '53' to each side of the equation. -53 + 53 + x = 54.258639865 + 53 Combine like terms: -53 + 53 = 0 0 + x = 54.258639865 + 53 x = 54.258639865 + 53 Combine like terms: 54.258639865 + 53 = 107.258639865 x = 107.258639865 Simplifying x = 107.258639865Subproblem 2
x + -53 = -54.258639865 Simplifying x + -53 = -54.258639865 Reorder the terms: -53 + x = -54.258639865 Solving -53 + x = -54.258639865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '53' to each side of the equation. -53 + 53 + x = -54.258639865 + 53 Combine like terms: -53 + 53 = 0 0 + x = -54.258639865 + 53 x = -54.258639865 + 53 Combine like terms: -54.258639865 + 53 = -1.258639865 x = -1.258639865 Simplifying x = -1.258639865Solution
The solution to the problem is based on the solutions from the subproblems. x = {107.258639865, -1.258639865}Solution
x = {0, 107.258639865, -1.258639865}
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