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Simplifying 10 = -0.1x2 + 2.4x + 8.1 Reorder the terms: 10 = 8.1 + 2.4x + -0.1x2 Solving 10 = 8.1 + 2.4x + -0.1x2 Solving for variable 'x'. Combine like terms: 10 + -8.1 = 1.9 1.9 + -2.4x + 0.1x2 = 8.1 + 2.4x + -0.1x2 + -8.1 + -2.4x + 0.1x2 Reorder the terms: 1.9 + -2.4x + 0.1x2 = 8.1 + -8.1 + 2.4x + -2.4x + -0.1x2 + 0.1x2 Combine like terms: 8.1 + -8.1 = 0.0 1.9 + -2.4x + 0.1x2 = 0.0 + 2.4x + -2.4x + -0.1x2 + 0.1x2 1.9 + -2.4x + 0.1x2 = 2.4x + -2.4x + -0.1x2 + 0.1x2 Combine like terms: 2.4x + -2.4x = 0.0 1.9 + -2.4x + 0.1x2 = 0.0 + -0.1x2 + 0.1x2 1.9 + -2.4x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 1.9 + -2.4x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 19 + -24x + x2 = 0 Move the constant term to the right: Add '-19' to each side of the equation. 19 + -24x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + -24x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -24x + x2 = 0 + -19 -24x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 -24x + x2 = -19 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -19 + 144 Reorder the terms: 144 + -24x + x2 = -19 + 144 Combine like terms: -19 + 144 = 125 144 + -24x + x2 = 125 Factor a perfect square on the left side: (x + -12)(x + -12) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + -12) equal to 11.180339887 and -11.180339887.Subproblem 1
x + -12 = 11.180339887 Simplifying x + -12 = 11.180339887 Reorder the terms: -12 + x = 11.180339887 Solving -12 + x = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 11.180339887 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.180339887 + 12 x = 11.180339887 + 12 Combine like terms: 11.180339887 + 12 = 23.180339887 x = 23.180339887 Simplifying x = 23.180339887Subproblem 2
x + -12 = -11.180339887 Simplifying x + -12 = -11.180339887 Reorder the terms: -12 + x = -11.180339887 Solving -12 + x = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -11.180339887 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.180339887 + 12 x = -11.180339887 + 12 Combine like terms: -11.180339887 + 12 = 0.819660113 x = 0.819660113 Simplifying x = 0.819660113Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.180339887, 0.819660113}
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