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Simplifying 1.75x2 + -31.75x + -105 = 0 Reorder the terms: -105 + -31.75x + 1.75x2 = 0 Solving -105 + -31.75x + 1.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.75 the coefficient of the squared term: Divide each side by '1.75'. -60 + -18.14285714x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -18.14285714x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -18.14285714x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -18.14285714x + x2 = 0 + 60 -18.14285714x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -18.14285714x + x2 = 60 The x term is -18.14285714x. Take half its coefficient (-9.07142857). Square it (82.29081630) and add it to both sides. Add '82.29081630' to each side of the equation. -18.14285714x + 82.29081630 + x2 = 60 + 82.29081630 Reorder the terms: 82.29081630 + -18.14285714x + x2 = 60 + 82.29081630 Combine like terms: 60 + 82.29081630 = 142.2908163 82.29081630 + -18.14285714x + x2 = 142.2908163 Factor a perfect square on the left side: (x + -9.07142857)(x + -9.07142857) = 142.2908163 Calculate the square root of the right side: 11.928571427 Break this problem into two subproblems by setting (x + -9.07142857) equal to 11.928571427 and -11.928571427.Subproblem 1
x + -9.07142857 = 11.928571427 Simplifying x + -9.07142857 = 11.928571427 Reorder the terms: -9.07142857 + x = 11.928571427 Solving -9.07142857 + x = 11.928571427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.07142857' to each side of the equation. -9.07142857 + 9.07142857 + x = 11.928571427 + 9.07142857 Combine like terms: -9.07142857 + 9.07142857 = 0.00000000 0.00000000 + x = 11.928571427 + 9.07142857 x = 11.928571427 + 9.07142857 Combine like terms: 11.928571427 + 9.07142857 = 20.999999997 x = 20.999999997 Simplifying x = 20.999999997Subproblem 2
x + -9.07142857 = -11.928571427 Simplifying x + -9.07142857 = -11.928571427 Reorder the terms: -9.07142857 + x = -11.928571427 Solving -9.07142857 + x = -11.928571427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.07142857' to each side of the equation. -9.07142857 + 9.07142857 + x = -11.928571427 + 9.07142857 Combine like terms: -9.07142857 + 9.07142857 = 0.00000000 0.00000000 + x = -11.928571427 + 9.07142857 x = -11.928571427 + 9.07142857 Combine like terms: -11.928571427 + 9.07142857 = -2.857142857 x = -2.857142857 Simplifying x = -2.857142857Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.999999997, -2.857142857}
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