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Simplifying 50 = -0.591x2 + 17.432x + -26.216 Reorder the terms: 50 = -26.216 + 17.432x + -0.591x2 Solving 50 = -26.216 + 17.432x + -0.591x2 Solving for variable 'x'. Combine like terms: 50 + 26.216 = 76.216 76.216 + -17.432x + 0.591x2 = -26.216 + 17.432x + -0.591x2 + 26.216 + -17.432x + 0.591x2 Reorder the terms: 76.216 + -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 76.216 + -17.432x + 0.591x2 = 0.000 + 17.432x + -17.432x + -0.591x2 + 0.591x2 76.216 + -17.432x + 0.591x2 = 17.432x + -17.432x + -0.591x2 + 0.591x2 Combine like terms: 17.432x + -17.432x = 0.000 76.216 + -17.432x + 0.591x2 = 0.000 + -0.591x2 + 0.591x2 76.216 + -17.432x + 0.591x2 = -0.591x2 + 0.591x2 Combine like terms: -0.591x2 + 0.591x2 = 0.000 76.216 + -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'. 128.9610829 + -29.49576988x + x2 = 0 Move the constant term to the right: Add '-128.9610829' to each side of the equation. 128.9610829 + -29.49576988x + -128.9610829 + x2 = 0 + -128.9610829 Reorder the terms: 128.9610829 + -128.9610829 + -29.49576988x + x2 = 0 + -128.9610829 Combine like terms: 128.9610829 + -128.9610829 = 0.0000000 0.0000000 + -29.49576988x + x2 = 0 + -128.9610829 -29.49576988x + x2 = 0 + -128.9610829 Combine like terms: 0 + -128.9610829 = -128.9610829 -29.49576988x + x2 = -128.9610829 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 = -128.9610829 + 217.5001102 Reorder the terms: 217.5001102 + -29.49576988x + x2 = -128.9610829 + 217.5001102 Combine like terms: -128.9610829 + 217.5001102 = 88.5390273 217.5001102 + -29.49576988x + x2 = 88.5390273 Factor a perfect square on the left side: (x + -14.74788494)(x + -14.74788494) = 88.5390273 Calculate the square root of the right side: 9.40951791 Break this problem into two subproblems by setting (x + -14.74788494) equal to 9.40951791 and -9.40951791.Subproblem 1
x + -14.74788494 = 9.40951791 Simplifying x + -14.74788494 = 9.40951791 Reorder the terms: -14.74788494 + x = 9.40951791 Solving -14.74788494 + x = 9.40951791 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 = 9.40951791 + 14.74788494 Combine like terms: -14.74788494 + 14.74788494 = 0.00000000 0.00000000 + x = 9.40951791 + 14.74788494 x = 9.40951791 + 14.74788494 Combine like terms: 9.40951791 + 14.74788494 = 24.15740285 x = 24.15740285 Simplifying x = 24.15740285Subproblem 2
x + -14.74788494 = -9.40951791 Simplifying x + -14.74788494 = -9.40951791 Reorder the terms: -14.74788494 + x = -9.40951791 Solving -14.74788494 + x = -9.40951791 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 = -9.40951791 + 14.74788494 Combine like terms: -14.74788494 + 14.74788494 = 0.00000000 0.00000000 + x = -9.40951791 + 14.74788494 x = -9.40951791 + 14.74788494 Combine like terms: -9.40951791 + 14.74788494 = 5.33836703 x = 5.33836703 Simplifying x = 5.33836703Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.15740285, 5.33836703}
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