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Simplifying 2x2 + -17x + -3 = 180 Reorder the terms: -3 + -17x + 2x2 = 180 Solving -3 + -17x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -3 + -180 + -17x + 2x2 = 180 + -180 Combine like terms: -3 + -180 = -183 -183 + -17x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -183 + -17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -91.5 + -8.5x + x2 = 0 Move the constant term to the right: Add '91.5' to each side of the equation. -91.5 + -8.5x + 91.5 + x2 = 0 + 91.5 Reorder the terms: -91.5 + 91.5 + -8.5x + x2 = 0 + 91.5 Combine like terms: -91.5 + 91.5 = 0.0 0.0 + -8.5x + x2 = 0 + 91.5 -8.5x + x2 = 0 + 91.5 Combine like terms: 0 + 91.5 = 91.5 -8.5x + x2 = 91.5 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 91.5 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 91.5 + 18.0625 Combine like terms: 91.5 + 18.0625 = 109.5625 18.0625 + -8.5x + x2 = 109.5625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 109.5625 Calculate the square root of the right side: 10.467210708 Break this problem into two subproblems by setting (x + -4.25) equal to 10.467210708 and -10.467210708.Subproblem 1
x + -4.25 = 10.467210708 Simplifying x + -4.25 = 10.467210708 Reorder the terms: -4.25 + x = 10.467210708 Solving -4.25 + x = 10.467210708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 10.467210708 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 10.467210708 + 4.25 x = 10.467210708 + 4.25 Combine like terms: 10.467210708 + 4.25 = 14.717210708 x = 14.717210708 Simplifying x = 14.717210708Subproblem 2
x + -4.25 = -10.467210708 Simplifying x + -4.25 = -10.467210708 Reorder the terms: -4.25 + x = -10.467210708 Solving -4.25 + x = -10.467210708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -10.467210708 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -10.467210708 + 4.25 x = -10.467210708 + 4.25 Combine like terms: -10.467210708 + 4.25 = -6.217210708 x = -6.217210708 Simplifying x = -6.217210708Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.717210708, -6.217210708}
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