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Simplifying 20 = -0.591x2 + 17.432x + -26.216 Reorder the terms: 20 = -26.216 + 17.432x + -0.591x2 Solving 20 = -26.216 + 17.432x + -0.591x2 Solving for variable 'x'. Combine like terms: 20 + 26.216 = 46.216 46.216 + -17.432x + 0.591x2 = -26.216 + 17.432x + -0.591x2 + 26.216 + -17.432x + 0.591x2 Reorder the terms: 46.216 + -17.432x + 0.591x2 = -26.216 + 26.216 + 17.432x + -17.432x + -0.591x2 + 0.591x2 Combine like terms: -26.216 + 26.216 = 0.000 46.216 + -17.432x + 0.591x2 = 0.000 + 17.432x + -17.432x + -0.591x2 + 0.591x2 46.216 + -17.432x + 0.591x2 = 17.432x + -17.432x + -0.591x2 + 0.591x2 Combine like terms: 17.432x + -17.432x = 0.000 46.216 + -17.432x + 0.591x2 = 0.000 + -0.591x2 + 0.591x2 46.216 + -17.432x + 0.591x2 = -0.591x2 + 0.591x2 Combine like terms: -0.591x2 + 0.591x2 = 0.000 46.216 + -17.432x + 0.591x2 = 0.000 Begin completing the square. Divide all terms by 0.591 the coefficient of the squared term: Divide each side by '0.591'. 78.19966159 + -29.49576988x + x2 = 0 Move the constant term to the right: Add '-78.19966159' to each side of the equation. 78.19966159 + -29.49576988x + -78.19966159 + x2 = 0 + -78.19966159 Reorder the terms: 78.19966159 + -78.19966159 + -29.49576988x + x2 = 0 + -78.19966159 Combine like terms: 78.19966159 + -78.19966159 = 0.00000000 0.00000000 + -29.49576988x + x2 = 0 + -78.19966159 -29.49576988x + x2 = 0 + -78.19966159 Combine like terms: 0 + -78.19966159 = -78.19966159 -29.49576988x + x2 = -78.19966159 The x term is -29.49576988x. Take half its coefficient (-14.74788494). Square it (217.5001102) and add it to both sides. Add '217.5001102' to each side of the equation. -29.49576988x + 217.5001102 + x2 = -78.19966159 + 217.5001102 Reorder the terms: 217.5001102 + -29.49576988x + x2 = -78.19966159 + 217.5001102 Combine like terms: -78.19966159 + 217.5001102 = 139.30044861 217.5001102 + -29.49576988x + x2 = 139.30044861 Factor a perfect square on the left side: (x + -14.74788494)(x + -14.74788494) = 139.30044861 Calculate the square root of the right side: 11.802561104 Break this problem into two subproblems by setting (x + -14.74788494) equal to 11.802561104 and -11.802561104.Subproblem 1
x + -14.74788494 = 11.802561104 Simplifying x + -14.74788494 = 11.802561104 Reorder the terms: -14.74788494 + x = 11.802561104 Solving -14.74788494 + x = 11.802561104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.74788494' to each side of the equation. -14.74788494 + 14.74788494 + x = 11.802561104 + 14.74788494 Combine like terms: -14.74788494 + 14.74788494 = 0.00000000 0.00000000 + x = 11.802561104 + 14.74788494 x = 11.802561104 + 14.74788494 Combine like terms: 11.802561104 + 14.74788494 = 26.550446044 x = 26.550446044 Simplifying x = 26.550446044Subproblem 2
x + -14.74788494 = -11.802561104 Simplifying x + -14.74788494 = -11.802561104 Reorder the terms: -14.74788494 + x = -11.802561104 Solving -14.74788494 + x = -11.802561104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.74788494' to each side of the equation. -14.74788494 + 14.74788494 + x = -11.802561104 + 14.74788494 Combine like terms: -14.74788494 + 14.74788494 = 0.00000000 0.00000000 + x = -11.802561104 + 14.74788494 x = -11.802561104 + 14.74788494 Combine like terms: -11.802561104 + 14.74788494 = 2.945323836 x = 2.945323836 Simplifying x = 2.945323836Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.550446044, 2.945323836}
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