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Simplifying 11 = 2x2 + 5x Reorder the terms: 11 = 5x + 2x2 Solving 11 = 5x + 2x2 Solving for variable 'x'. Reorder the terms: 11 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2 Combine like terms: 5x + -5x = 0 11 + -5x + -2x2 = 0 + 2x2 + -2x2 11 + -5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 11 + -5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 2.5x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 2.5x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 2.5x + x2 = 0 + 5.5 2.5x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 2.5x + x2 = 5.5 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 = 5.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 5.5 + 1.5625 Combine like terms: 5.5 + 1.5625 = 7.0625 1.5625 + 2.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + 1.25) equal to 2.657536453 and -2.657536453.Subproblem 1
x + 1.25 = 2.657536453 Simplifying x + 1.25 = 2.657536453 Reorder the terms: 1.25 + x = 2.657536453 Solving 1.25 + x = 2.657536453 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 = 2.657536453 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.657536453 + -1.25 x = 2.657536453 + -1.25 Combine like terms: 2.657536453 + -1.25 = 1.407536453 x = 1.407536453 Simplifying x = 1.407536453Subproblem 2
x + 1.25 = -2.657536453 Simplifying x + 1.25 = -2.657536453 Reorder the terms: 1.25 + x = -2.657536453 Solving 1.25 + x = -2.657536453 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 = -2.657536453 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.657536453 + -1.25 x = -2.657536453 + -1.25 Combine like terms: -2.657536453 + -1.25 = -3.907536453 x = -3.907536453 Simplifying x = -3.907536453Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.407536453, -3.907536453}
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