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Simplifying 4x3 + 3x2 + -60x = 0 Reorder the terms: -60x + 3x2 + 4x3 = 0 Solving -60x + 3x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-60 + 3x + 4x2) = 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 '(-60 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying -60 + 3x + 4x2 = 0 Solving -60 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -15 + 0.75x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 0.75x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 0.75x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 0.75x + x2 = 0 + 15 0.75x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 0.75x + x2 = 15 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 15 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 15 + 0.140625 Combine like terms: 15 + 0.140625 = 15.140625 0.140625 + 0.75x + x2 = 15.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 15.140625 Calculate the square root of the right side: 3.891095604 Break this problem into two subproblems by setting (x + 0.375) equal to 3.891095604 and -3.891095604.Subproblem 1
x + 0.375 = 3.891095604 Simplifying x + 0.375 = 3.891095604 Reorder the terms: 0.375 + x = 3.891095604 Solving 0.375 + x = 3.891095604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 3.891095604 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 3.891095604 + -0.375 x = 3.891095604 + -0.375 Combine like terms: 3.891095604 + -0.375 = 3.516095604 x = 3.516095604 Simplifying x = 3.516095604Subproblem 2
x + 0.375 = -3.891095604 Simplifying x + 0.375 = -3.891095604 Reorder the terms: 0.375 + x = -3.891095604 Solving 0.375 + x = -3.891095604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -3.891095604 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -3.891095604 + -0.375 x = -3.891095604 + -0.375 Combine like terms: -3.891095604 + -0.375 = -4.266095604 x = -4.266095604 Simplifying x = -4.266095604Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.516095604, -4.266095604}Solution
x = {0, 3.516095604, -4.266095604}
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