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Simplifying 54 + -30x = 400x2 Solving 54 + -30x = 400x2 Solving for variable 'x'. Combine like terms: 400x2 + -400x2 = 0 54 + -30x + -400x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -15x + -200x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + -15x + -200x2)' equal to zero and attempt to solve: Simplifying 27 + -15x + -200x2 = 0 Solving 27 + -15x + -200x2 = 0 Begin completing the square. Divide all terms by -200 the coefficient of the squared term: Divide each side by '-200'. -0.135 + 0.075x + x2 = 0.00 Move the constant term to the right: Add '0.135' to each side of the equation. -0.135 + 0.075x + 0.135 + x2 = 0.00 + 0.135 Reorder the terms: -0.135 + 0.135 + 0.075x + x2 = 0.00 + 0.135 Combine like terms: -0.135 + 0.135 = 0.000 0.000 + 0.075x + x2 = 0.00 + 0.135 0.075x + x2 = 0.00 + 0.135 Combine like terms: 0.00 + 0.135 = 0.135 0.075x + x2 = 0.135 The x term is 0.075x. Take half its coefficient (0.0375). Square it (0.00140625) and add it to both sides. Add '0.00140625' to each side of the equation. 0.075x + 0.00140625 + x2 = 0.135 + 0.00140625 Reorder the terms: 0.00140625 + 0.075x + x2 = 0.135 + 0.00140625 Combine like terms: 0.135 + 0.00140625 = 0.13640625 0.00140625 + 0.075x + x2 = 0.13640625 Factor a perfect square on the left side: (x + 0.0375)(x + 0.0375) = 0.13640625 Calculate the square root of the right side: 0.369332168 Break this problem into two subproblems by setting (x + 0.0375) equal to 0.369332168 and -0.369332168.Subproblem 1
x + 0.0375 = 0.369332168 Simplifying x + 0.0375 = 0.369332168 Reorder the terms: 0.0375 + x = 0.369332168 Solving 0.0375 + x = 0.369332168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0375' to each side of the equation. 0.0375 + -0.0375 + x = 0.369332168 + -0.0375 Combine like terms: 0.0375 + -0.0375 = 0.0000 0.0000 + x = 0.369332168 + -0.0375 x = 0.369332168 + -0.0375 Combine like terms: 0.369332168 + -0.0375 = 0.331832168 x = 0.331832168 Simplifying x = 0.331832168Subproblem 2
x + 0.0375 = -0.369332168 Simplifying x + 0.0375 = -0.369332168 Reorder the terms: 0.0375 + x = -0.369332168 Solving 0.0375 + x = -0.369332168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0375' to each side of the equation. 0.0375 + -0.0375 + x = -0.369332168 + -0.0375 Combine like terms: 0.0375 + -0.0375 = 0.0000 0.0000 + x = -0.369332168 + -0.0375 x = -0.369332168 + -0.0375 Combine like terms: -0.369332168 + -0.0375 = -0.406832168 x = -0.406832168 Simplifying x = -0.406832168Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.331832168, -0.406832168}Solution
x = {0.331832168, -0.406832168}
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