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Simplifying -0.125x2 + 2x + -6 = 1.4 Reorder the terms: -6 + 2x + -0.125x2 = 1.4 Solving -6 + 2x + -0.125x2 = 1.4 Solving for variable 'x'. Reorder the terms: -6 + -1.4 + 2x + -0.125x2 = 1.4 + -1.4 Combine like terms: -6 + -1.4 = -7.4 -7.4 + 2x + -0.125x2 = 1.4 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 -7.4 + 2x + -0.125x2 = 0.0 Begin completing the square. Divide all terms by -0.125 the coefficient of the squared term: Divide each side by '-0.125'. 59.2 + -16x + x2 = 0 Move the constant term to the right: Add '-59.2' to each side of the equation. 59.2 + -16x + -59.2 + x2 = 0 + -59.2 Reorder the terms: 59.2 + -59.2 + -16x + x2 = 0 + -59.2 Combine like terms: 59.2 + -59.2 = 0.0 0.0 + -16x + x2 = 0 + -59.2 -16x + x2 = 0 + -59.2 Combine like terms: 0 + -59.2 = -59.2 -16x + x2 = -59.2 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -59.2 + 64 Reorder the terms: 64 + -16x + x2 = -59.2 + 64 Combine like terms: -59.2 + 64 = 4.8 64 + -16x + x2 = 4.8 Factor a perfect square on the left side: (x + -8)(x + -8) = 4.8 Calculate the square root of the right side: 2.19089023 Break this problem into two subproblems by setting (x + -8) equal to 2.19089023 and -2.19089023.Subproblem 1
x + -8 = 2.19089023 Simplifying x + -8 = 2.19089023 Reorder the terms: -8 + x = 2.19089023 Solving -8 + x = 2.19089023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 2.19089023 + 8 Combine like terms: -8 + 8 = 0 0 + x = 2.19089023 + 8 x = 2.19089023 + 8 Combine like terms: 2.19089023 + 8 = 10.19089023 x = 10.19089023 Simplifying x = 10.19089023Subproblem 2
x + -8 = -2.19089023 Simplifying x + -8 = -2.19089023 Reorder the terms: -8 + x = -2.19089023 Solving -8 + x = -2.19089023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -2.19089023 + 8 Combine like terms: -8 + 8 = 0 0 + x = -2.19089023 + 8 x = -2.19089023 + 8 Combine like terms: -2.19089023 + 8 = 5.80910977 x = 5.80910977 Simplifying x = 5.80910977Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.19089023, 5.80910977}
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