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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 = -1.78778555 x = -1.78778555 Simplifying x = -1.78778555Subproblem 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 = -6.71221445 x = -6.71221445 Simplifying x = -6.71221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.78778555, -6.71221445}
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