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Simplifying x2 = 8.5x + -15 Reorder the terms: x2 = -15 + 8.5x Solving x2 = -15 + 8.5x Solving for variable 'x'. Reorder the terms: 15 + -8.5x + x2 = -15 + 8.5x + 15 + -8.5x Reorder the terms: 15 + -8.5x + x2 = -15 + 15 + 8.5x + -8.5x Combine like terms: -15 + 15 = 0 15 + -8.5x + x2 = 0 + 8.5x + -8.5x 15 + -8.5x + x2 = 8.5x + -8.5x Combine like terms: 8.5x + -8.5x = 0.0 15 + -8.5x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -8.5x + -15 + x2 = 0.0 + -15 Reorder the terms: 15 + -15 + -8.5x + x2 = 0.0 + -15 Combine like terms: 15 + -15 = 0 0 + -8.5x + x2 = 0.0 + -15 -8.5x + x2 = 0.0 + -15 Combine like terms: 0.0 + -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 = 6 x = 6 Simplifying x = 6Subproblem 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 = 2.5 x = 2.5 Simplifying x = 2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, 2.5}
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