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Simplifying x2 + 15x + -58 = 0 Reorder the terms: -58 + 15x + x2 = 0 Solving -58 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + 15x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + 15x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 15x + x2 = 0 + 58 15x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 15x + x2 = 58 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 58 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 58 + 56.25 Combine like terms: 58 + 56.25 = 114.25 56.25 + 15x + x2 = 114.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 114.25 Calculate the square root of the right side: 10.688779163 Break this problem into two subproblems by setting (x + 7.5) equal to 10.688779163 and -10.688779163.Subproblem 1
x + 7.5 = 10.688779163 Simplifying x + 7.5 = 10.688779163 Reorder the terms: 7.5 + x = 10.688779163 Solving 7.5 + x = 10.688779163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 10.688779163 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 10.688779163 + -7.5 x = 10.688779163 + -7.5 Combine like terms: 10.688779163 + -7.5 = 3.188779163 x = 3.188779163 Simplifying x = 3.188779163Subproblem 2
x + 7.5 = -10.688779163 Simplifying x + 7.5 = -10.688779163 Reorder the terms: 7.5 + x = -10.688779163 Solving 7.5 + x = -10.688779163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -10.688779163 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -10.688779163 + -7.5 x = -10.688779163 + -7.5 Combine like terms: -10.688779163 + -7.5 = -18.188779163 x = -18.188779163 Simplifying x = -18.188779163Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.188779163, -18.188779163}
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