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Simplifying 116.26 = 1516.3x + 26.84x2 Solving 116.26 = 1516.3x + 26.84x2 Solving for variable 'x'. Reorder the terms: 116.26 + -1516.3x + -26.84x2 = 1516.3x + -1516.3x + 26.84x2 + -26.84x2 Combine like terms: 1516.3x + -1516.3x = 0.0 116.26 + -1516.3x + -26.84x2 = 0.0 + 26.84x2 + -26.84x2 116.26 + -1516.3x + -26.84x2 = 26.84x2 + -26.84x2 Combine like terms: 26.84x2 + -26.84x2 = 0.00 116.26 + -1516.3x + -26.84x2 = 0.00 Begin completing the square. Divide all terms by -26.84 the coefficient of the squared term: Divide each side by '-26.84'. -4.331594635 + 56.49403875x + x2 = 0 Move the constant term to the right: Add '4.331594635' to each side of the equation. -4.331594635 + 56.49403875x + 4.331594635 + x2 = 0 + 4.331594635 Reorder the terms: -4.331594635 + 4.331594635 + 56.49403875x + x2 = 0 + 4.331594635 Combine like terms: -4.331594635 + 4.331594635 = 0.000000000 0.000000000 + 56.49403875x + x2 = 0 + 4.331594635 56.49403875x + x2 = 0 + 4.331594635 Combine like terms: 0 + 4.331594635 = 4.331594635 56.49403875x + x2 = 4.331594635 The x term is 56.49403875x. Take half its coefficient (28.24701938). Square it (797.8941039) and add it to both sides. Add '797.8941039' to each side of the equation. 56.49403875x + 797.8941039 + x2 = 4.331594635 + 797.8941039 Reorder the terms: 797.8941039 + 56.49403875x + x2 = 4.331594635 + 797.8941039 Combine like terms: 4.331594635 + 797.8941039 = 802.225698535 797.8941039 + 56.49403875x + x2 = 802.225698535 Factor a perfect square on the left side: (x + 28.24701938)(x + 28.24701938) = 802.225698535 Calculate the square root of the right side: 28.323589083 Break this problem into two subproblems by setting (x + 28.24701938) equal to 28.323589083 and -28.323589083.Subproblem 1
x + 28.24701938 = 28.323589083 Simplifying x + 28.24701938 = 28.323589083 Reorder the terms: 28.24701938 + x = 28.323589083 Solving 28.24701938 + x = 28.323589083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28.24701938' to each side of the equation. 28.24701938 + -28.24701938 + x = 28.323589083 + -28.24701938 Combine like terms: 28.24701938 + -28.24701938 = 0.00000000 0.00000000 + x = 28.323589083 + -28.24701938 x = 28.323589083 + -28.24701938 Combine like terms: 28.323589083 + -28.24701938 = 0.076569703 x = 0.076569703 Simplifying x = 0.076569703Subproblem 2
x + 28.24701938 = -28.323589083 Simplifying x + 28.24701938 = -28.323589083 Reorder the terms: 28.24701938 + x = -28.323589083 Solving 28.24701938 + x = -28.323589083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28.24701938' to each side of the equation. 28.24701938 + -28.24701938 + x = -28.323589083 + -28.24701938 Combine like terms: 28.24701938 + -28.24701938 = 0.00000000 0.00000000 + x = -28.323589083 + -28.24701938 x = -28.323589083 + -28.24701938 Combine like terms: -28.323589083 + -28.24701938 = -56.570608463 x = -56.570608463 Simplifying x = -56.570608463Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.076569703, -56.570608463}
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