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Simplifying 2x * x + 11x + 26 = 59 Multiply x * x 2x2 + 11x + 26 = 59 Reorder the terms: 26 + 11x + 2x2 = 59 Solving 26 + 11x + 2x2 = 59 Solving for variable 'x'. Reorder the terms: 26 + -59 + 11x + 2x2 = 59 + -59 Combine like terms: 26 + -59 = -33 -33 + 11x + 2x2 = 59 + -59 Combine like terms: 59 + -59 = 0 -33 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + 5.5x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + 5.5x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + 5.5x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + 5.5x + x2 = 0 + 16.5 5.5x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 5.5x + x2 = 16.5 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 16.5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 16.5 + 7.5625 Combine like terms: 16.5 + 7.5625 = 24.0625 7.5625 + 5.5x + x2 = 24.0625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (x + 2.75) equal to 4.905354218 and -4.905354218.Subproblem 1
x + 2.75 = 4.905354218 Simplifying x + 2.75 = 4.905354218 Reorder the terms: 2.75 + x = 4.905354218 Solving 2.75 + x = 4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 4.905354218 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 4.905354218 + -2.75 x = 4.905354218 + -2.75 Combine like terms: 4.905354218 + -2.75 = 2.155354218 x = 2.155354218 Simplifying x = 2.155354218Subproblem 2
x + 2.75 = -4.905354218 Simplifying x + 2.75 = -4.905354218 Reorder the terms: 2.75 + x = -4.905354218 Solving 2.75 + x = -4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -4.905354218 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -4.905354218 + -2.75 x = -4.905354218 + -2.75 Combine like terms: -4.905354218 + -2.75 = -7.655354218 x = -7.655354218 Simplifying x = -7.655354218Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.155354218, -7.655354218}
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