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Simplifying 0.08x2 + -0.08x + -11.5 = 0 Reorder the terms: -11.5 + -0.08x + 0.08x2 = 0 Solving -11.5 + -0.08x + 0.08x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. -143.75 + -1x + x2 = 0 Move the constant term to the right: Add '143.75' to each side of the equation. -143.75 + -1x + 143.75 + x2 = 0 + 143.75 Reorder the terms: -143.75 + 143.75 + -1x + x2 = 0 + 143.75 Combine like terms: -143.75 + 143.75 = 0.00 0.00 + -1x + x2 = 0 + 143.75 -1x + x2 = 0 + 143.75 Combine like terms: 0 + 143.75 = 143.75 -1x + x2 = 143.75 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 143.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 143.75 + 0.25 Combine like terms: 143.75 + 0.25 = 144 0.25 + -1x + x2 = 144 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 144 Calculate the square root of the right side: 12 Break this problem into two subproblems by setting (x + -0.5) equal to 12 and -12.Subproblem 1
x + -0.5 = 12 Simplifying x + -0.5 = 12 Reorder the terms: -0.5 + x = 12 Solving -0.5 + x = 12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 12 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 12 + 0.5 x = 12 + 0.5 Combine like terms: 12 + 0.5 = 12.5 x = 12.5 Simplifying x = 12.5Subproblem 2
x + -0.5 = -12 Simplifying x + -0.5 = -12 Reorder the terms: -0.5 + x = -12 Solving -0.5 + x = -12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -12 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -12 + 0.5 x = -12 + 0.5 Combine like terms: -12 + 0.5 = -11.5 x = -11.5 Simplifying x = -11.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.5, -11.5}
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