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Simplifying x2 + 15x + 12 = 0 Reorder the terms: 12 + 15x + x2 = 0 Solving 12 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 15x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 15x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 15x + x2 = 0 + -12 15x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 15x + x2 = -12 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 = -12 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -12 + 56.25 Combine like terms: -12 + 56.25 = 44.25 56.25 + 15x + x2 = 44.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + 7.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + 7.5 = 6.652067348 Simplifying x + 7.5 = 6.652067348 Reorder the terms: 7.5 + x = 6.652067348 Solving 7.5 + x = 6.652067348 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 = 6.652067348 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 6.652067348 + -7.5 x = 6.652067348 + -7.5 Combine like terms: 6.652067348 + -7.5 = -0.847932652 x = -0.847932652 Simplifying x = -0.847932652Subproblem 2
x + 7.5 = -6.652067348 Simplifying x + 7.5 = -6.652067348 Reorder the terms: 7.5 + x = -6.652067348 Solving 7.5 + x = -6.652067348 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 = -6.652067348 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -6.652067348 + -7.5 x = -6.652067348 + -7.5 Combine like terms: -6.652067348 + -7.5 = -14.152067348 x = -14.152067348 Simplifying x = -14.152067348Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.847932652, -14.152067348}
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