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Simplifying x = -0.6(-65 + 18x + -1x2) x = (-65 * -0.6 + 18x * -0.6 + -1x2 * -0.6) x = (39 + -10.8x + 0.6x2) Solving x = 39 + -10.8x + 0.6x2 Solving for variable 'x'. Reorder the terms: -39 + x + 10.8x + -0.6x2 = 39 + -10.8x + 0.6x2 + -39 + 10.8x + -0.6x2 Combine like terms: x + 10.8x = 11.8x -39 + 11.8x + -0.6x2 = 39 + -10.8x + 0.6x2 + -39 + 10.8x + -0.6x2 Reorder the terms: -39 + 11.8x + -0.6x2 = 39 + -39 + -10.8x + 10.8x + 0.6x2 + -0.6x2 Combine like terms: 39 + -39 = 0 -39 + 11.8x + -0.6x2 = 0 + -10.8x + 10.8x + 0.6x2 + -0.6x2 -39 + 11.8x + -0.6x2 = -10.8x + 10.8x + 0.6x2 + -0.6x2 Combine like terms: -10.8x + 10.8x = 0.0 -39 + 11.8x + -0.6x2 = 0.0 + 0.6x2 + -0.6x2 -39 + 11.8x + -0.6x2 = 0.6x2 + -0.6x2 Combine like terms: 0.6x2 + -0.6x2 = 0.0 -39 + 11.8x + -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'. 65 + -19.66666667x + x2 = 0 Move the constant term to the right: Add '-65' to each side of the equation. 65 + -19.66666667x + -65 + x2 = 0 + -65 Reorder the terms: 65 + -65 + -19.66666667x + x2 = 0 + -65 Combine like terms: 65 + -65 = 0 0 + -19.66666667x + x2 = 0 + -65 -19.66666667x + x2 = 0 + -65 Combine like terms: 0 + -65 = -65 -19.66666667x + x2 = -65 The x term is -19.66666667x. Take half its coefficient (-9.833333335). Square it (96.69444448) and add it to both sides. Add '96.69444448' to each side of the equation. -19.66666667x + 96.69444448 + x2 = -65 + 96.69444448 Reorder the terms: 96.69444448 + -19.66666667x + x2 = -65 + 96.69444448 Combine like terms: -65 + 96.69444448 = 31.69444448 96.69444448 + -19.66666667x + x2 = 31.69444448 Factor a perfect square on the left side: (x + -9.833333335)(x + -9.833333335) = 31.69444448 Calculate the square root of the right side: 5.629781921 Break this problem into two subproblems by setting (x + -9.833333335) equal to 5.629781921 and -5.629781921.Subproblem 1
x + -9.833333335 = 5.629781921 Simplifying x + -9.833333335 = 5.629781921 Reorder the terms: -9.833333335 + x = 5.629781921 Solving -9.833333335 + x = 5.629781921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.833333335' to each side of the equation. -9.833333335 + 9.833333335 + x = 5.629781921 + 9.833333335 Combine like terms: -9.833333335 + 9.833333335 = 0.000000000 0.000000000 + x = 5.629781921 + 9.833333335 x = 5.629781921 + 9.833333335 Combine like terms: 5.629781921 + 9.833333335 = 15.463115256 x = 15.463115256 Simplifying x = 15.463115256Subproblem 2
x + -9.833333335 = -5.629781921 Simplifying x + -9.833333335 = -5.629781921 Reorder the terms: -9.833333335 + x = -5.629781921 Solving -9.833333335 + x = -5.629781921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.833333335' to each side of the equation. -9.833333335 + 9.833333335 + x = -5.629781921 + 9.833333335 Combine like terms: -9.833333335 + 9.833333335 = 0.000000000 0.000000000 + x = -5.629781921 + 9.833333335 x = -5.629781921 + 9.833333335 Combine like terms: -5.629781921 + 9.833333335 = 4.203551414 x = 4.203551414 Simplifying x = 4.203551414Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.463115256, 4.203551414}
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