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Simplifying x = -0.6x2 + -13x + 72 Reorder the terms: x = 72 + -13x + -0.6x2 Solving x = 72 + -13x + -0.6x2 Solving for variable 'x'. Reorder the terms: -72 + x + 13x + 0.6x2 = 72 + -13x + -0.6x2 + -72 + 13x + 0.6x2 Combine like terms: x + 13x = 14x -72 + 14x + 0.6x2 = 72 + -13x + -0.6x2 + -72 + 13x + 0.6x2 Reorder the terms: -72 + 14x + 0.6x2 = 72 + -72 + -13x + 13x + -0.6x2 + 0.6x2 Combine like terms: 72 + -72 = 0 -72 + 14x + 0.6x2 = 0 + -13x + 13x + -0.6x2 + 0.6x2 -72 + 14x + 0.6x2 = -13x + 13x + -0.6x2 + 0.6x2 Combine like terms: -13x + 13x = 0 -72 + 14x + 0.6x2 = 0 + -0.6x2 + 0.6x2 -72 + 14x + 0.6x2 = -0.6x2 + 0.6x2 Combine like terms: -0.6x2 + 0.6x2 = 0.0 -72 + 14x + 0.6x2 = 0.0 Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -120 + 23.33333333x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 23.33333333x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 23.33333333x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 23.33333333x + x2 = 0 + 120 23.33333333x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 23.33333333x + x2 = 120 The x term is 23.33333333x. Take half its coefficient (11.66666667). Square it (136.1111112) and add it to both sides. Add '136.1111112' to each side of the equation. 23.33333333x + 136.1111112 + x2 = 120 + 136.1111112 Reorder the terms: 136.1111112 + 23.33333333x + x2 = 120 + 136.1111112 Combine like terms: 120 + 136.1111112 = 256.1111112 136.1111112 + 23.33333333x + x2 = 256.1111112 Factor a perfect square on the left side: (x + 11.66666667)(x + 11.66666667) = 256.1111112 Calculate the square root of the right side: 16.003471848 Break this problem into two subproblems by setting (x + 11.66666667) equal to 16.003471848 and -16.003471848.Subproblem 1
x + 11.66666667 = 16.003471848 Simplifying x + 11.66666667 = 16.003471848 Reorder the terms: 11.66666667 + x = 16.003471848 Solving 11.66666667 + x = 16.003471848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.66666667' to each side of the equation. 11.66666667 + -11.66666667 + x = 16.003471848 + -11.66666667 Combine like terms: 11.66666667 + -11.66666667 = 0.00000000 0.00000000 + x = 16.003471848 + -11.66666667 x = 16.003471848 + -11.66666667 Combine like terms: 16.003471848 + -11.66666667 = 4.336805178 x = 4.336805178 Simplifying x = 4.336805178Subproblem 2
x + 11.66666667 = -16.003471848 Simplifying x + 11.66666667 = -16.003471848 Reorder the terms: 11.66666667 + x = -16.003471848 Solving 11.66666667 + x = -16.003471848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.66666667' to each side of the equation. 11.66666667 + -11.66666667 + x = -16.003471848 + -11.66666667 Combine like terms: 11.66666667 + -11.66666667 = 0.00000000 0.00000000 + x = -16.003471848 + -11.66666667 x = -16.003471848 + -11.66666667 Combine like terms: -16.003471848 + -11.66666667 = -27.670138518 x = -27.670138518 Simplifying x = -27.670138518Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.336805178, -27.670138518}
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