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Simplifying 0 = x2 + 58x + 29 Reorder the terms: 0 = 29 + 58x + x2 Solving 0 = 29 + 58x + x2 Solving for variable 'x'. Combine like terms: 0 + -29 = -29 -29 + -58x + -1x2 = 29 + 58x + x2 + -29 + -58x + -1x2 Reorder the terms: -29 + -58x + -1x2 = 29 + -29 + 58x + -58x + x2 + -1x2 Combine like terms: 29 + -29 = 0 -29 + -58x + -1x2 = 0 + 58x + -58x + x2 + -1x2 -29 + -58x + -1x2 = 58x + -58x + x2 + -1x2 Combine like terms: 58x + -58x = 0 -29 + -58x + -1x2 = 0 + x2 + -1x2 -29 + -58x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -29 + -58x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(29 + 58x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(29 + 58x + x2)' equal to zero and attempt to solve: Simplifying 29 + 58x + x2 = 0 Solving 29 + 58x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 58x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + 58x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 58x + x2 = 0 + -29 58x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 58x + x2 = -29 The x term is 58x. Take half its coefficient (29). Square it (841) and add it to both sides. Add '841' to each side of the equation. 58x + 841 + x2 = -29 + 841 Reorder the terms: 841 + 58x + x2 = -29 + 841 Combine like terms: -29 + 841 = 812 841 + 58x + x2 = 812 Factor a perfect square on the left side: (x + 29)(x + 29) = 812 Calculate the square root of the right side: 28.495613698 Break this problem into two subproblems by setting (x + 29) equal to 28.495613698 and -28.495613698.Subproblem 1
x + 29 = 28.495613698 Simplifying x + 29 = 28.495613698 Reorder the terms: 29 + x = 28.495613698 Solving 29 + x = 28.495613698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + x = 28.495613698 + -29 Combine like terms: 29 + -29 = 0 0 + x = 28.495613698 + -29 x = 28.495613698 + -29 Combine like terms: 28.495613698 + -29 = -0.504386302 x = -0.504386302 Simplifying x = -0.504386302Subproblem 2
x + 29 = -28.495613698 Simplifying x + 29 = -28.495613698 Reorder the terms: 29 + x = -28.495613698 Solving 29 + x = -28.495613698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + x = -28.495613698 + -29 Combine like terms: 29 + -29 = 0 0 + x = -28.495613698 + -29 x = -28.495613698 + -29 Combine like terms: -28.495613698 + -29 = -57.495613698 x = -57.495613698 Simplifying x = -57.495613698Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.504386302, -57.495613698}Solution
x = {-0.504386302, -57.495613698}
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