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Simplifying 9x3 + 25x = 40x2 Reorder the terms: 25x + 9x3 = 40x2 Solving 25x + 9x3 = 40x2 Solving for variable 'x'. Reorder the terms: 25x + -40x2 + 9x3 = 40x2 + -40x2 Combine like terms: 40x2 + -40x2 = 0 25x + -40x2 + 9x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(25 + -40x + 9x2) = 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 '(25 + -40x + 9x2)' equal to zero and attempt to solve: Simplifying 25 + -40x + 9x2 = 0 Solving 25 + -40x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.777777778 + -4.444444444x + x2 = 0 Move the constant term to the right: Add '-2.777777778' to each side of the equation. 2.777777778 + -4.444444444x + -2.777777778 + x2 = 0 + -2.777777778 Reorder the terms: 2.777777778 + -2.777777778 + -4.444444444x + x2 = 0 + -2.777777778 Combine like terms: 2.777777778 + -2.777777778 = 0.000000000 0.000000000 + -4.444444444x + x2 = 0 + -2.777777778 -4.444444444x + x2 = 0 + -2.777777778 Combine like terms: 0 + -2.777777778 = -2.777777778 -4.444444444x + x2 = -2.777777778 The x term is -4.444444444x. Take half its coefficient (-2.222222222). Square it (4.938271604) and add it to both sides. Add '4.938271604' to each side of the equation. -4.444444444x + 4.938271604 + x2 = -2.777777778 + 4.938271604 Reorder the terms: 4.938271604 + -4.444444444x + x2 = -2.777777778 + 4.938271604 Combine like terms: -2.777777778 + 4.938271604 = 2.160493826 4.938271604 + -4.444444444x + x2 = 2.160493826 Factor a perfect square on the left side: (x + -2.222222222)(x + -2.222222222) = 2.160493826 Calculate the square root of the right side: 1.469861839 Break this problem into two subproblems by setting (x + -2.222222222) equal to 1.469861839 and -1.469861839.Subproblem 1
x + -2.222222222 = 1.469861839 Simplifying x + -2.222222222 = 1.469861839 Reorder the terms: -2.222222222 + x = 1.469861839 Solving -2.222222222 + x = 1.469861839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + x = 1.469861839 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = 1.469861839 + 2.222222222 x = 1.469861839 + 2.222222222 Combine like terms: 1.469861839 + 2.222222222 = 3.692084061 x = 3.692084061 Simplifying x = 3.692084061Subproblem 2
x + -2.222222222 = -1.469861839 Simplifying x + -2.222222222 = -1.469861839 Reorder the terms: -2.222222222 + x = -1.469861839 Solving -2.222222222 + x = -1.469861839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + x = -1.469861839 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = -1.469861839 + 2.222222222 x = -1.469861839 + 2.222222222 Combine like terms: -1.469861839 + 2.222222222 = 0.752360383 x = 0.752360383 Simplifying x = 0.752360383Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.692084061, 0.752360383}Solution
x = {0, 3.692084061, 0.752360383}
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