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Simplifying x2 + 8.5x + 13 = 0 Reorder the terms: 13 + 8.5x + x2 = 0 Solving 13 + 8.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 8.5x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 8.5x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 8.5x + x2 = 0 + -13 8.5x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 8.5x + x2 = -13 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 = -13 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -13 + 18.0625 Combine like terms: -13 + 18.0625 = 5.0625 18.0625 + 8.5x + x2 = 5.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (x + 4.25) equal to 2.25 and -2.25.Subproblem 1
x + 4.25 = 2.25 Simplifying x + 4.25 = 2.25 Reorder the terms: 4.25 + x = 2.25 Solving 4.25 + x = 2.25 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 = 2.25 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 2.25 + -4.25 x = 2.25 + -4.25 Combine like terms: 2.25 + -4.25 = -2 x = -2 Simplifying x = -2Subproblem 2
x + 4.25 = -2.25 Simplifying x + 4.25 = -2.25 Reorder the terms: 4.25 + x = -2.25 Solving 4.25 + x = -2.25 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 = -2.25 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -2.25 + -4.25 x = -2.25 + -4.25 Combine like terms: -2.25 + -4.25 = -6.5 x = -6.5 Simplifying x = -6.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2, -6.5}
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