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Simplifying x2 + 15x = -5 Reorder the terms: 15x + x2 = -5 Solving 15x + x2 = -5 Solving for variable 'x'. Reorder the terms: 5 + 15x + x2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 15x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 15x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 15x + x2 = 0 + -5 15x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 15x + x2 = -5 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 = -5 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -5 + 56.25 Combine like terms: -5 + 56.25 = 51.25 56.25 + 15x + x2 = 51.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + 7.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + 7.5 = 7.158910532 Simplifying x + 7.5 = 7.158910532 Reorder the terms: 7.5 + x = 7.158910532 Solving 7.5 + x = 7.158910532 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 = 7.158910532 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.158910532 + -7.5 x = 7.158910532 + -7.5 Combine like terms: 7.158910532 + -7.5 = -0.341089468 x = -0.341089468 Simplifying x = -0.341089468Subproblem 2
x + 7.5 = -7.158910532 Simplifying x + 7.5 = -7.158910532 Reorder the terms: 7.5 + x = -7.158910532 Solving 7.5 + x = -7.158910532 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 = -7.158910532 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.158910532 + -7.5 x = -7.158910532 + -7.5 Combine like terms: -7.158910532 + -7.5 = -14.658910532 x = -14.658910532 Simplifying x = -14.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.341089468, -14.658910532}
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