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Simplifying x2 + -85x + -158 = 0 Reorder the terms: -158 + -85x + x2 = 0 Solving -158 + -85x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '158' to each side of the equation. -158 + -85x + 158 + x2 = 0 + 158 Reorder the terms: -158 + 158 + -85x + x2 = 0 + 158 Combine like terms: -158 + 158 = 0 0 + -85x + x2 = 0 + 158 -85x + x2 = 0 + 158 Combine like terms: 0 + 158 = 158 -85x + x2 = 158 The x term is -85x. Take half its coefficient (-42.5). Square it (1806.25) and add it to both sides. Add '1806.25' to each side of the equation. -85x + 1806.25 + x2 = 158 + 1806.25 Reorder the terms: 1806.25 + -85x + x2 = 158 + 1806.25 Combine like terms: 158 + 1806.25 = 1964.25 1806.25 + -85x + x2 = 1964.25 Factor a perfect square on the left side: (x + -42.5)(x + -42.5) = 1964.25 Calculate the square root of the right side: 44.319860108 Break this problem into two subproblems by setting (x + -42.5) equal to 44.319860108 and -44.319860108.Subproblem 1
x + -42.5 = 44.319860108 Simplifying x + -42.5 = 44.319860108 Reorder the terms: -42.5 + x = 44.319860108 Solving -42.5 + x = 44.319860108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.5' to each side of the equation. -42.5 + 42.5 + x = 44.319860108 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x = 44.319860108 + 42.5 x = 44.319860108 + 42.5 Combine like terms: 44.319860108 + 42.5 = 86.819860108 x = 86.819860108 Simplifying x = 86.819860108Subproblem 2
x + -42.5 = -44.319860108 Simplifying x + -42.5 = -44.319860108 Reorder the terms: -42.5 + x = -44.319860108 Solving -42.5 + x = -44.319860108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.5' to each side of the equation. -42.5 + 42.5 + x = -44.319860108 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x = -44.319860108 + 42.5 x = -44.319860108 + 42.5 Combine like terms: -44.319860108 + 42.5 = -1.819860108 x = -1.819860108 Simplifying x = -1.819860108Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.819860108, -1.819860108}
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