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Simplifying 2x2 + -17x + 24 = 0 Reorder the terms: 24 + -17x + 2x2 = 0 Solving 24 + -17x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12 + -8.5x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -8.5x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -8.5x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -8.5x + x2 = 0 + -12 -8.5x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -8.5x + x2 = -12 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 = -12 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -12 + 18.0625 Combine like terms: -12 + 18.0625 = 6.0625 18.0625 + -8.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -4.25) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -4.25 = 2.46221445 Simplifying x + -4.25 = 2.46221445 Reorder the terms: -4.25 + x = 2.46221445 Solving -4.25 + x = 2.46221445 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 = 2.46221445 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 2.46221445 + 4.25 x = 2.46221445 + 4.25 Combine like terms: 2.46221445 + 4.25 = 6.71221445 x = 6.71221445 Simplifying x = 6.71221445Subproblem 2
x + -4.25 = -2.46221445 Simplifying x + -4.25 = -2.46221445 Reorder the terms: -4.25 + x = -2.46221445 Solving -4.25 + x = -2.46221445 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 = -2.46221445 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -2.46221445 + 4.25 x = -2.46221445 + 4.25 Combine like terms: -2.46221445 + 4.25 = 1.78778555 x = 1.78778555 Simplifying x = 1.78778555Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.71221445, 1.78778555}
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