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Simplifying 2500x2 + 390x + -58 = 0 Reorder the terms: -58 + 390x + 2500x2 = 0 Solving -58 + 390x + 2500x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + 195x + 1250x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + 195x + 1250x2)' equal to zero and attempt to solve: Simplifying -29 + 195x + 1250x2 = 0 Solving -29 + 195x + 1250x2 = 0 Begin completing the square. Divide all terms by 1250 the coefficient of the squared term: Divide each side by '1250'. -0.0232 + 0.156x + x2 = 0.0 Move the constant term to the right: Add '0.0232' to each side of the equation. -0.0232 + 0.156x + 0.0232 + x2 = 0.0 + 0.0232 Reorder the terms: -0.0232 + 0.0232 + 0.156x + x2 = 0.0 + 0.0232 Combine like terms: -0.0232 + 0.0232 = 0.0000 0.0000 + 0.156x + x2 = 0.0 + 0.0232 0.156x + x2 = 0.0 + 0.0232 Combine like terms: 0.0 + 0.0232 = 0.0232 0.156x + x2 = 0.0232 The x term is 0.156x. Take half its coefficient (0.078). Square it (0.006084) and add it to both sides. Add '0.006084' to each side of the equation. 0.156x + 0.006084 + x2 = 0.0232 + 0.006084 Reorder the terms: 0.006084 + 0.156x + x2 = 0.0232 + 0.006084 Combine like terms: 0.0232 + 0.006084 = 0.029284 0.006084 + 0.156x + x2 = 0.029284 Factor a perfect square on the left side: (x + 0.078)(x + 0.078) = 0.029284 Calculate the square root of the right side: 0.171125685 Break this problem into two subproblems by setting (x + 0.078) equal to 0.171125685 and -0.171125685.Subproblem 1
x + 0.078 = 0.171125685 Simplifying x + 0.078 = 0.171125685 Reorder the terms: 0.078 + x = 0.171125685 Solving 0.078 + x = 0.171125685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.078' to each side of the equation. 0.078 + -0.078 + x = 0.171125685 + -0.078 Combine like terms: 0.078 + -0.078 = 0.000 0.000 + x = 0.171125685 + -0.078 x = 0.171125685 + -0.078 Combine like terms: 0.171125685 + -0.078 = 0.093125685 x = 0.093125685 Simplifying x = 0.093125685Subproblem 2
x + 0.078 = -0.171125685 Simplifying x + 0.078 = -0.171125685 Reorder the terms: 0.078 + x = -0.171125685 Solving 0.078 + x = -0.171125685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.078' to each side of the equation. 0.078 + -0.078 + x = -0.171125685 + -0.078 Combine like terms: 0.078 + -0.078 = 0.000 0.000 + x = -0.171125685 + -0.078 x = -0.171125685 + -0.078 Combine like terms: -0.171125685 + -0.078 = -0.249125685 x = -0.249125685 Simplifying x = -0.249125685Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.093125685, -0.249125685}Solution
x = {0.093125685, -0.249125685}
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