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Simplifying x2 + 8.5x + 15 = 0 Reorder the terms: 15 + 8.5x + x2 = 0 Solving 15 + 8.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 8.5x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 8.5x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 8.5x + x2 = 0 + -15 8.5x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 8.5x + x2 = -15 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = -15 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -15 + 18.0625 Combine like terms: -15 + 18.0625 = 3.0625 18.0625 + 8.5x + x2 = 3.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 3.0625 Calculate the square root of the right side: 1.75 Break this problem into two subproblems by setting (x + 4.25) equal to 1.75 and -1.75.Subproblem 1
x + 4.25 = 1.75 Simplifying x + 4.25 = 1.75 Reorder the terms: 4.25 + x = 1.75 Solving 4.25 + x = 1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 1.75 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 1.75 + -4.25 x = 1.75 + -4.25 Combine like terms: 1.75 + -4.25 = -2.5 x = -2.5 Simplifying x = -2.5Subproblem 2
x + 4.25 = -1.75 Simplifying x + 4.25 = -1.75 Reorder the terms: 4.25 + x = -1.75 Solving 4.25 + x = -1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -1.75 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -1.75 + -4.25 x = -1.75 + -4.25 Combine like terms: -1.75 + -4.25 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.5, -6}
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