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Simplifying 4x2 + 90x + -350 = 0 Reorder the terms: -350 + 90x + 4x2 = 0 Solving -350 + 90x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-175 + 45x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-175 + 45x + 2x2)' equal to zero and attempt to solve: Simplifying -175 + 45x + 2x2 = 0 Solving -175 + 45x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -87.5 + 22.5x + x2 = 0 Move the constant term to the right: Add '87.5' to each side of the equation. -87.5 + 22.5x + 87.5 + x2 = 0 + 87.5 Reorder the terms: -87.5 + 87.5 + 22.5x + x2 = 0 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + 22.5x + x2 = 0 + 87.5 22.5x + x2 = 0 + 87.5 Combine like terms: 0 + 87.5 = 87.5 22.5x + x2 = 87.5 The x term is 22.5x. Take half its coefficient (11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. 22.5x + 126.5625 + x2 = 87.5 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = 87.5 + 126.5625 Combine like terms: 87.5 + 126.5625 = 214.0625 126.5625 + 22.5x + x2 = 214.0625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 214.0625 Calculate the square root of the right side: 14.630874888 Break this problem into two subproblems by setting (x + 11.25) equal to 14.630874888 and -14.630874888.Subproblem 1
x + 11.25 = 14.630874888 Simplifying x + 11.25 = 14.630874888 Reorder the terms: 11.25 + x = 14.630874888 Solving 11.25 + x = 14.630874888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = 14.630874888 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 14.630874888 + -11.25 x = 14.630874888 + -11.25 Combine like terms: 14.630874888 + -11.25 = 3.380874888 x = 3.380874888 Simplifying x = 3.380874888Subproblem 2
x + 11.25 = -14.630874888 Simplifying x + 11.25 = -14.630874888 Reorder the terms: 11.25 + x = -14.630874888 Solving 11.25 + x = -14.630874888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = -14.630874888 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -14.630874888 + -11.25 x = -14.630874888 + -11.25 Combine like terms: -14.630874888 + -11.25 = -25.880874888 x = -25.880874888 Simplifying x = -25.880874888Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.380874888, -25.880874888}Solution
x = {3.380874888, -25.880874888}
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