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Simplifying 2x2 + -35 = 17x Reorder the terms: -35 + 2x2 = 17x Solving -35 + 2x2 = 17x Solving for variable 'x'. Reorder the terms: -35 + -17x + 2x2 = 17x + -17x Combine like terms: 17x + -17x = 0 -35 + -17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -8.5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -8.5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -8.5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -8.5x + x2 = 0 + 17.5 -8.5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -8.5x + x2 = 17.5 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 = 17.5 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 17.5 + 18.0625 Combine like terms: 17.5 + 18.0625 = 35.5625 18.0625 + -8.5x + x2 = 35.5625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 35.5625 Calculate the square root of the right side: 5.963430221 Break this problem into two subproblems by setting (x + -4.25) equal to 5.963430221 and -5.963430221.Subproblem 1
x + -4.25 = 5.963430221 Simplifying x + -4.25 = 5.963430221 Reorder the terms: -4.25 + x = 5.963430221 Solving -4.25 + x = 5.963430221 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 = 5.963430221 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 5.963430221 + 4.25 x = 5.963430221 + 4.25 Combine like terms: 5.963430221 + 4.25 = 10.213430221 x = 10.213430221 Simplifying x = 10.213430221Subproblem 2
x + -4.25 = -5.963430221 Simplifying x + -4.25 = -5.963430221 Reorder the terms: -4.25 + x = -5.963430221 Solving -4.25 + x = -5.963430221 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 = -5.963430221 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -5.963430221 + 4.25 x = -5.963430221 + 4.25 Combine like terms: -5.963430221 + 4.25 = -1.713430221 x = -1.713430221 Simplifying x = -1.713430221Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.213430221, -1.713430221}
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