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Simplifying 2x2 + -5x + 6 = 32 Reorder the terms: 6 + -5x + 2x2 = 32 Solving 6 + -5x + 2x2 = 32 Solving for variable 'x'. Reorder the terms: 6 + -32 + -5x + 2x2 = 32 + -32 Combine like terms: 6 + -32 = -26 -26 + -5x + 2x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -26 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13 + -2.5x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -2.5x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -2.5x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2.5x + x2 = 0 + 13 -2.5x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -2.5x + x2 = 13 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 = 13 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 13 + 1.5625 Combine like terms: 13 + 1.5625 = 14.5625 1.5625 + -2.5x + x2 = 14.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (x + -1.25) equal to 3.816084381 and -3.816084381.Subproblem 1
x + -1.25 = 3.816084381 Simplifying x + -1.25 = 3.816084381 Reorder the terms: -1.25 + x = 3.816084381 Solving -1.25 + x = 3.816084381 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 = 3.816084381 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.816084381 + 1.25 x = 3.816084381 + 1.25 Combine like terms: 3.816084381 + 1.25 = 5.066084381 x = 5.066084381 Simplifying x = 5.066084381Subproblem 2
x + -1.25 = -3.816084381 Simplifying x + -1.25 = -3.816084381 Reorder the terms: -1.25 + x = -3.816084381 Solving -1.25 + x = -3.816084381 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 = -3.816084381 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.816084381 + 1.25 x = -3.816084381 + 1.25 Combine like terms: -3.816084381 + 1.25 = -2.566084381 x = -2.566084381 Simplifying x = -2.566084381Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.066084381, -2.566084381}
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