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Simplifying -0.125x2 + x + 42 = 5 Reorder the terms: 42 + x + -0.125x2 = 5 Solving 42 + x + -0.125x2 = 5 Solving for variable 'x'. Reorder the terms: 42 + -5 + x + -0.125x2 = 5 + -5 Combine like terms: 42 + -5 = 37 37 + x + -0.125x2 = 5 + -5 Combine like terms: 5 + -5 = 0 37 + x + -0.125x2 = 0 Begin completing the square. Divide all terms by -0.125 the coefficient of the squared term: Divide each side by '-0.125'. -296 + -8x + x2 = 0 Move the constant term to the right: Add '296' to each side of the equation. -296 + -8x + 296 + x2 = 0 + 296 Reorder the terms: -296 + 296 + -8x + x2 = 0 + 296 Combine like terms: -296 + 296 = 0 0 + -8x + x2 = 0 + 296 -8x + x2 = 0 + 296 Combine like terms: 0 + 296 = 296 -8x + x2 = 296 The x term is x. 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. -8x + 0.25 + x2 = 296 + 0.25 Reorder the terms: 0.25 + -8x + x2 = 296 + 0.25 Combine like terms: 296 + 0.25 = 296.25 0.25 + -8x + x2 = 296.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 296.25 Calculate the square root of the right side: 17.211914478 Break this problem into two subproblems by setting (x + 0.5) equal to 17.211914478 and -17.211914478.Subproblem 1
x + 0.5 = 17.211914478 Simplifying x + 0.5 = 17.211914478 Reorder the terms: 0.5 + x = 17.211914478 Solving 0.5 + x = 17.211914478 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 = 17.211914478 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 17.211914478 + -0.5 x = 17.211914478 + -0.5 Combine like terms: 17.211914478 + -0.5 = 16.711914478 x = 16.711914478 Simplifying x = 16.711914478Subproblem 2
x + 0.5 = -17.211914478 Simplifying x + 0.5 = -17.211914478 Reorder the terms: 0.5 + x = -17.211914478 Solving 0.5 + x = -17.211914478 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 = -17.211914478 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -17.211914478 + -0.5 x = -17.211914478 + -0.5 Combine like terms: -17.211914478 + -0.5 = -17.711914478 x = -17.711914478 Simplifying x = -17.711914478Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.711914478, -17.711914478}
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