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Simplifying 144x3 + 212x2 + -40x = 0 Reorder the terms: -40x + 212x2 + 144x3 = 0 Solving -40x + 212x2 + 144x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-10 + 53x + 36x2) = 0 Ignore the factor 4.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 '(-10 + 53x + 36x2)' equal to zero and attempt to solve: Simplifying -10 + 53x + 36x2 = 0 Solving -10 + 53x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.2777777778 + 1.472222222x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + 1.472222222x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + 1.472222222x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + 1.472222222x + x2 = 0 + 0.2777777778 1.472222222x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 1.472222222x + x2 = 0.2777777778 The x term is 1.472222222x. Take half its coefficient (0.736111111). Square it (0.5418595677) and add it to both sides. Add '0.5418595677' to each side of the equation. 1.472222222x + 0.5418595677 + x2 = 0.2777777778 + 0.5418595677 Reorder the terms: 0.5418595677 + 1.472222222x + x2 = 0.2777777778 + 0.5418595677 Combine like terms: 0.2777777778 + 0.5418595677 = 0.8196373455 0.5418595677 + 1.472222222x + x2 = 0.8196373455 Factor a perfect square on the left side: (x + 0.736111111)(x + 0.736111111) = 0.8196373455 Calculate the square root of the right side: 0.905338249 Break this problem into two subproblems by setting (x + 0.736111111) equal to 0.905338249 and -0.905338249.Subproblem 1
x + 0.736111111 = 0.905338249 Simplifying x + 0.736111111 = 0.905338249 Reorder the terms: 0.736111111 + x = 0.905338249 Solving 0.736111111 + x = 0.905338249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.736111111' to each side of the equation. 0.736111111 + -0.736111111 + x = 0.905338249 + -0.736111111 Combine like terms: 0.736111111 + -0.736111111 = 0.000000000 0.000000000 + x = 0.905338249 + -0.736111111 x = 0.905338249 + -0.736111111 Combine like terms: 0.905338249 + -0.736111111 = 0.169227138 x = 0.169227138 Simplifying x = 0.169227138Subproblem 2
x + 0.736111111 = -0.905338249 Simplifying x + 0.736111111 = -0.905338249 Reorder the terms: 0.736111111 + x = -0.905338249 Solving 0.736111111 + x = -0.905338249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.736111111' to each side of the equation. 0.736111111 + -0.736111111 + x = -0.905338249 + -0.736111111 Combine like terms: 0.736111111 + -0.736111111 = 0.000000000 0.000000000 + x = -0.905338249 + -0.736111111 x = -0.905338249 + -0.736111111 Combine like terms: -0.905338249 + -0.736111111 = -1.64144936 x = -1.64144936 Simplifying x = -1.64144936Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.169227138, -1.64144936}Solution
x = {0, 0.169227138, -1.64144936}
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