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Simplifying x2 + 15x + -188 = 0 Reorder the terms: -188 + 15x + x2 = 0 Solving -188 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '188' to each side of the equation. -188 + 15x + 188 + x2 = 0 + 188 Reorder the terms: -188 + 188 + 15x + x2 = 0 + 188 Combine like terms: -188 + 188 = 0 0 + 15x + x2 = 0 + 188 15x + x2 = 0 + 188 Combine like terms: 0 + 188 = 188 15x + x2 = 188 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 = 188 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 188 + 56.25 Combine like terms: 188 + 56.25 = 244.25 56.25 + 15x + x2 = 244.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 244.25 Calculate the square root of the right side: 15.628499608 Break this problem into two subproblems by setting (x + 7.5) equal to 15.628499608 and -15.628499608.Subproblem 1
x + 7.5 = 15.628499608 Simplifying x + 7.5 = 15.628499608 Reorder the terms: 7.5 + x = 15.628499608 Solving 7.5 + x = 15.628499608 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 = 15.628499608 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 15.628499608 + -7.5 x = 15.628499608 + -7.5 Combine like terms: 15.628499608 + -7.5 = 8.128499608 x = 8.128499608 Simplifying x = 8.128499608Subproblem 2
x + 7.5 = -15.628499608 Simplifying x + 7.5 = -15.628499608 Reorder the terms: 7.5 + x = -15.628499608 Solving 7.5 + x = -15.628499608 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 = -15.628499608 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -15.628499608 + -7.5 x = -15.628499608 + -7.5 Combine like terms: -15.628499608 + -7.5 = -23.128499608 x = -23.128499608 Simplifying x = -23.128499608Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.128499608, -23.128499608}
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