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Simplifying 9x4 + -240x3 + 16x2 = 0 Reorder the terms: 16x2 + -240x3 + 9x4 = 0 Solving 16x2 + -240x3 + 9x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(16 + -240x + 9x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(16 + -240x + 9x2)' equal to zero and attempt to solve: Simplifying 16 + -240x + 9x2 = 0 Solving 16 + -240x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.777777778 + -26.66666667x + x2 = 0 Move the constant term to the right: Add '-1.777777778' to each side of the equation. 1.777777778 + -26.66666667x + -1.777777778 + x2 = 0 + -1.777777778 Reorder the terms: 1.777777778 + -1.777777778 + -26.66666667x + x2 = 0 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + -26.66666667x + x2 = 0 + -1.777777778 -26.66666667x + x2 = 0 + -1.777777778 Combine like terms: 0 + -1.777777778 = -1.777777778 -26.66666667x + x2 = -1.777777778 The x term is -26.66666667x. Take half its coefficient (-13.33333334). Square it (177.7777780) and add it to both sides. Add '177.7777780' to each side of the equation. -26.66666667x + 177.7777780 + x2 = -1.777777778 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667x + x2 = -1.777777778 + 177.7777780 Combine like terms: -1.777777778 + 177.7777780 = 176.000000222 177.7777780 + -26.66666667x + x2 = 176.000000222 Factor a perfect square on the left side: (x + -13.33333334)(x + -13.33333334) = 176.000000222 Calculate the square root of the right side: 13.26649917 Break this problem into two subproblems by setting (x + -13.33333334) equal to 13.26649917 and -13.26649917.Subproblem 1
x + -13.33333334 = 13.26649917 Simplifying x + -13.33333334 = 13.26649917 Reorder the terms: -13.33333334 + x = 13.26649917 Solving -13.33333334 + x = 13.26649917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + x = 13.26649917 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = 13.26649917 + 13.33333334 x = 13.26649917 + 13.33333334 Combine like terms: 13.26649917 + 13.33333334 = 26.59983251 x = 26.59983251 Simplifying x = 26.59983251Subproblem 2
x + -13.33333334 = -13.26649917 Simplifying x + -13.33333334 = -13.26649917 Reorder the terms: -13.33333334 + x = -13.26649917 Solving -13.33333334 + x = -13.26649917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + x = -13.26649917 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = -13.26649917 + 13.33333334 x = -13.26649917 + 13.33333334 Combine like terms: -13.26649917 + 13.33333334 = 0.06683417 x = 0.06683417 Simplifying x = 0.06683417Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.59983251, 0.06683417}Solution
x = {0, 26.59983251, 0.06683417}
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