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Simplifying 17x2 + -56x + -112 = 0 Reorder the terms: -112 + -56x + 17x2 = 0 Solving -112 + -56x + 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'. -6.588235294 + -3.294117647x + x2 = 0 Move the constant term to the right: Add '6.588235294' to each side of the equation. -6.588235294 + -3.294117647x + 6.588235294 + x2 = 0 + 6.588235294 Reorder the terms: -6.588235294 + 6.588235294 + -3.294117647x + x2 = 0 + 6.588235294 Combine like terms: -6.588235294 + 6.588235294 = 0.000000000 0.000000000 + -3.294117647x + x2 = 0 + 6.588235294 -3.294117647x + x2 = 0 + 6.588235294 Combine like terms: 0 + 6.588235294 = 6.588235294 -3.294117647x + x2 = 6.588235294 The x term is -3.294117647x. Take half its coefficient (-1.647058824). Square it (2.712802770) and add it to both sides. Add '2.712802770' to each side of the equation. -3.294117647x + 2.712802770 + x2 = 6.588235294 + 2.712802770 Reorder the terms: 2.712802770 + -3.294117647x + x2 = 6.588235294 + 2.712802770 Combine like terms: 6.588235294 + 2.712802770 = 9.301038064 2.712802770 + -3.294117647x + x2 = 9.301038064 Factor a perfect square on the left side: (x + -1.647058824)(x + -1.647058824) = 9.301038064 Calculate the square root of the right side: 3.049760329 Break this problem into two subproblems by setting (x + -1.647058824) equal to 3.049760329 and -3.049760329.Subproblem 1
x + -1.647058824 = 3.049760329 Simplifying x + -1.647058824 = 3.049760329 Reorder the terms: -1.647058824 + x = 3.049760329 Solving -1.647058824 + x = 3.049760329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.647058824' to each side of the equation. -1.647058824 + 1.647058824 + x = 3.049760329 + 1.647058824 Combine like terms: -1.647058824 + 1.647058824 = 0.000000000 0.000000000 + x = 3.049760329 + 1.647058824 x = 3.049760329 + 1.647058824 Combine like terms: 3.049760329 + 1.647058824 = 4.696819153 x = 4.696819153 Simplifying x = 4.696819153Subproblem 2
x + -1.647058824 = -3.049760329 Simplifying x + -1.647058824 = -3.049760329 Reorder the terms: -1.647058824 + x = -3.049760329 Solving -1.647058824 + x = -3.049760329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.647058824' to each side of the equation. -1.647058824 + 1.647058824 + x = -3.049760329 + 1.647058824 Combine like terms: -1.647058824 + 1.647058824 = 0.000000000 0.000000000 + x = -3.049760329 + 1.647058824 x = -3.049760329 + 1.647058824 Combine like terms: -3.049760329 + 1.647058824 = -1.402701505 x = -1.402701505 Simplifying x = -1.402701505Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.696819153, -1.402701505}
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