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Simplifying 4x3 + 10x2 + -12x = 0 Reorder the terms: -12x + 10x2 + 4x3 = 0 Solving -12x + 10x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-6 + 5x + 2x2) = 0 Ignore the factor 2.Subproblem 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 '(-6 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying -6 + 5x + 2x2 = 0 Solving -6 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 2.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.5x + x2 = 0 + 3 2.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.5x + x2 = 3 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 3 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 3 + 1.5625 Combine like terms: 3 + 1.5625 = 4.5625 1.5625 + 2.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + 1.25) equal to 2.136000936 and -2.136000936.Subproblem 1
x + 1.25 = 2.136000936 Simplifying x + 1.25 = 2.136000936 Reorder the terms: 1.25 + x = 2.136000936 Solving 1.25 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.136000936 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.136000936 + -1.25 x = 2.136000936 + -1.25 Combine like terms: 2.136000936 + -1.25 = 0.886000936 x = 0.886000936 Simplifying x = 0.886000936Subproblem 2
x + 1.25 = -2.136000936 Simplifying x + 1.25 = -2.136000936 Reorder the terms: 1.25 + x = -2.136000936 Solving 1.25 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.136000936 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.136000936 + -1.25 x = -2.136000936 + -1.25 Combine like terms: -2.136000936 + -1.25 = -3.386000936 x = -3.386000936 Simplifying x = -3.386000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.886000936, -3.386000936}Solution
x = {0, 0.886000936, -3.386000936}
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