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Simplifying x = 0.0048x3 + -0.0054x2 Reorder the terms: x = -0.0054x2 + 0.0048x3 Solving x = -0.0054x2 + 0.0048x3 Solving for variable 'x'. Reorder the terms: x + 0.0054x2 + -0.0048x3 = -0.0054x2 + 0.0054x2 + 0.0048x3 + -0.0048x3 Combine like terms: -0.0054x2 + 0.0054x2 = 0.0000 x + 0.0054x2 + -0.0048x3 = 0.0000 + 0.0048x3 + -0.0048x3 x + 0.0054x2 + -0.0048x3 = 0.0048x3 + -0.0048x3 Combine like terms: 0.0048x3 + -0.0048x3 = 0.0000 x + 0.0054x2 + -0.0048x3 = 0.0000 Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 0.0054x + -0.0048x2) = 0.0000Subproblem 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 '(1 + 0.0054x + -0.0048x2)' equal to zero and attempt to solve: Simplifying 1 + 0.0054x + -0.0048x2 = 0 Solving 1 + 0.0054x + -0.0048x2 = 0 Begin completing the square. Divide all terms by -0.0048 the coefficient of the squared term: Divide each side by '-0.0048'. -208.3333333 + -1.125x + x2 = 0 Move the constant term to the right: Add '208.3333333' to each side of the equation. -208.3333333 + -1.125x + 208.3333333 + x2 = 0 + 208.3333333 Reorder the terms: -208.3333333 + 208.3333333 + -1.125x + x2 = 0 + 208.3333333 Combine like terms: -208.3333333 + 208.3333333 = 0.0000000 0.0000000 + -1.125x + x2 = 0 + 208.3333333 -1.125x + x2 = 0 + 208.3333333 Combine like terms: 0 + 208.3333333 = 208.3333333 -1.125x + x2 = 208.3333333 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = 208.3333333 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 208.3333333 + 0.31640625 Combine like terms: 208.3333333 + 0.31640625 = 208.64973955 0.31640625 + -1.125x + x2 = 208.64973955 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 208.64973955 Calculate the square root of the right side: 14.444713204 Break this problem into two subproblems by setting (x + -0.5625) equal to 14.444713204 and -14.444713204.Subproblem 1
x + -0.5625 = 14.444713204 Simplifying x + -0.5625 = 14.444713204 Reorder the terms: -0.5625 + x = 14.444713204 Solving -0.5625 + x = 14.444713204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 14.444713204 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 14.444713204 + 0.5625 x = 14.444713204 + 0.5625 Combine like terms: 14.444713204 + 0.5625 = 15.007213204 x = 15.007213204 Simplifying x = 15.007213204Subproblem 2
x + -0.5625 = -14.444713204 Simplifying x + -0.5625 = -14.444713204 Reorder the terms: -0.5625 + x = -14.444713204 Solving -0.5625 + x = -14.444713204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -14.444713204 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -14.444713204 + 0.5625 x = -14.444713204 + 0.5625 Combine like terms: -14.444713204 + 0.5625 = -13.882213204 x = -13.882213204 Simplifying x = -13.882213204Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.007213204, -13.882213204}Solution
x = {0, 15.007213204, -13.882213204}
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