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Simplifying 17x2 + -140x + 115 = 0 Reorder the terms: 115 + -140x + 17x2 = 0 Solving 115 + -140x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 6.764705882 + -8.235294118x + x2 = 0 Move the constant term to the right: Add '-6.764705882' to each side of the equation. 6.764705882 + -8.235294118x + -6.764705882 + x2 = 0 + -6.764705882 Reorder the terms: 6.764705882 + -6.764705882 + -8.235294118x + x2 = 0 + -6.764705882 Combine like terms: 6.764705882 + -6.764705882 = 0.000000000 0.000000000 + -8.235294118x + x2 = 0 + -6.764705882 -8.235294118x + x2 = 0 + -6.764705882 Combine like terms: 0 + -6.764705882 = -6.764705882 -8.235294118x + x2 = -6.764705882 The x term is -8.235294118x. Take half its coefficient (-4.117647059). Square it (16.95501730) and add it to both sides. Add '16.95501730' to each side of the equation. -8.235294118x + 16.95501730 + x2 = -6.764705882 + 16.95501730 Reorder the terms: 16.95501730 + -8.235294118x + x2 = -6.764705882 + 16.95501730 Combine like terms: -6.764705882 + 16.95501730 = 10.190311418 16.95501730 + -8.235294118x + x2 = 10.190311418 Factor a perfect square on the left side: (x + -4.117647059)(x + -4.117647059) = 10.190311418 Calculate the square root of the right side: 3.192226718 Break this problem into two subproblems by setting (x + -4.117647059) equal to 3.192226718 and -3.192226718.Subproblem 1
x + -4.117647059 = 3.192226718 Simplifying x + -4.117647059 = 3.192226718 Reorder the terms: -4.117647059 + x = 3.192226718 Solving -4.117647059 + x = 3.192226718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.117647059' to each side of the equation. -4.117647059 + 4.117647059 + x = 3.192226718 + 4.117647059 Combine like terms: -4.117647059 + 4.117647059 = 0.000000000 0.000000000 + x = 3.192226718 + 4.117647059 x = 3.192226718 + 4.117647059 Combine like terms: 3.192226718 + 4.117647059 = 7.309873777 x = 7.309873777 Simplifying x = 7.309873777Subproblem 2
x + -4.117647059 = -3.192226718 Simplifying x + -4.117647059 = -3.192226718 Reorder the terms: -4.117647059 + x = -3.192226718 Solving -4.117647059 + x = -3.192226718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.117647059' to each side of the equation. -4.117647059 + 4.117647059 + x = -3.192226718 + 4.117647059 Combine like terms: -4.117647059 + 4.117647059 = 0.000000000 0.000000000 + x = -3.192226718 + 4.117647059 x = -3.192226718 + 4.117647059 Combine like terms: -3.192226718 + 4.117647059 = 0.925420341 x = 0.925420341 Simplifying x = 0.925420341Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.309873777, 0.925420341}
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