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Simplifying 2x2 + -5x + -17 = 12 Reorder the terms: -17 + -5x + 2x2 = 12 Solving -17 + -5x + 2x2 = 12 Solving for variable 'x'. Reorder the terms: -17 + -12 + -5x + 2x2 = 12 + -12 Combine like terms: -17 + -12 = -29 -29 + -5x + 2x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -29 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + -2.5x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + -2.5x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + -2.5x + x2 = 0 + 14.5 -2.5x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 -2.5x + x2 = 14.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 14.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 14.5 + 1.5625 Combine like terms: 14.5 + 1.5625 = 16.0625 1.5625 + -2.5x + x2 = 16.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 16.0625 Calculate the square root of the right side: 4.007804885 Break this problem into two subproblems by setting (x + -1.25) equal to 4.007804885 and -4.007804885.Subproblem 1
x + -1.25 = 4.007804885 Simplifying x + -1.25 = 4.007804885 Reorder the terms: -1.25 + x = 4.007804885 Solving -1.25 + x = 4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 4.007804885 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 4.007804885 + 1.25 x = 4.007804885 + 1.25 Combine like terms: 4.007804885 + 1.25 = 5.257804885 x = 5.257804885 Simplifying x = 5.257804885Subproblem 2
x + -1.25 = -4.007804885 Simplifying x + -1.25 = -4.007804885 Reorder the terms: -1.25 + x = -4.007804885 Solving -1.25 + x = -4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -4.007804885 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -4.007804885 + 1.25 x = -4.007804885 + 1.25 Combine like terms: -4.007804885 + 1.25 = -2.757804885 x = -2.757804885 Simplifying x = -2.757804885Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.257804885, -2.757804885}
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