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Simplifying 4x3 + -150x2 + 900x = 450x Reorder the terms: 900x + -150x2 + 4x3 = 450x Solving 900x + -150x2 + 4x3 = 450x Solving for variable 'x'. Reorder the terms: 900x + -450x + -150x2 + 4x3 = 450x + -450x Combine like terms: 900x + -450x = 450x 450x + -150x2 + 4x3 = 450x + -450x Combine like terms: 450x + -450x = 0 450x + -150x2 + 4x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(225 + -75x + 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 '(225 + -75x + 2x2)' equal to zero and attempt to solve: Simplifying 225 + -75x + 2x2 = 0 Solving 225 + -75x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 112.5 + -37.5x + x2 = 0 Move the constant term to the right: Add '-112.5' to each side of the equation. 112.5 + -37.5x + -112.5 + x2 = 0 + -112.5 Reorder the terms: 112.5 + -112.5 + -37.5x + x2 = 0 + -112.5 Combine like terms: 112.5 + -112.5 = 0.0 0.0 + -37.5x + x2 = 0 + -112.5 -37.5x + x2 = 0 + -112.5 Combine like terms: 0 + -112.5 = -112.5 -37.5x + x2 = -112.5 The x term is -37.5x. Take half its coefficient (-18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. -37.5x + 351.5625 + x2 = -112.5 + 351.5625 Reorder the terms: 351.5625 + -37.5x + x2 = -112.5 + 351.5625 Combine like terms: -112.5 + 351.5625 = 239.0625 351.5625 + -37.5x + x2 = 239.0625 Factor a perfect square on the left side: (x + -18.75)(x + -18.75) = 239.0625 Calculate the square root of the right side: 15.461646096 Break this problem into two subproblems by setting (x + -18.75) equal to 15.461646096 and -15.461646096.Subproblem 1
x + -18.75 = 15.461646096 Simplifying x + -18.75 = 15.461646096 Reorder the terms: -18.75 + x = 15.461646096 Solving -18.75 + x = 15.461646096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + x = 15.461646096 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = 15.461646096 + 18.75 x = 15.461646096 + 18.75 Combine like terms: 15.461646096 + 18.75 = 34.211646096 x = 34.211646096 Simplifying x = 34.211646096Subproblem 2
x + -18.75 = -15.461646096 Simplifying x + -18.75 = -15.461646096 Reorder the terms: -18.75 + x = -15.461646096 Solving -18.75 + x = -15.461646096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + x = -15.461646096 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = -15.461646096 + 18.75 x = -15.461646096 + 18.75 Combine like terms: -15.461646096 + 18.75 = 3.288353904 x = 3.288353904 Simplifying x = 3.288353904Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.211646096, 3.288353904}Solution
x = {0, 34.211646096, 3.288353904}
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