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Simplifying 11x2 + -6x = 15 Reorder the terms: -6x + 11x2 = 15 Solving -6x + 11x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -6x + 11x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -6x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.363636364 + -0.5454545455x + x2 = 0 Move the constant term to the right: Add '1.363636364' to each side of the equation. -1.363636364 + -0.5454545455x + 1.363636364 + x2 = 0 + 1.363636364 Reorder the terms: -1.363636364 + 1.363636364 + -0.5454545455x + x2 = 0 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + -0.5454545455x + x2 = 0 + 1.363636364 -0.5454545455x + x2 = 0 + 1.363636364 Combine like terms: 0 + 1.363636364 = 1.363636364 -0.5454545455x + x2 = 1.363636364 The x term is -0.5454545455x. Take half its coefficient (-0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. -0.5454545455x + 0.07438016533 + x2 = 1.363636364 + 0.07438016533 Reorder the terms: 0.07438016533 + -0.5454545455x + x2 = 1.363636364 + 0.07438016533 Combine like terms: 1.363636364 + 0.07438016533 = 1.43801652933 0.07438016533 + -0.5454545455x + x2 = 1.43801652933 Factor a perfect square on the left side: (x + -0.2727272728)(x + -0.2727272728) = 1.43801652933 Calculate the square root of the right side: 1.199173269 Break this problem into two subproblems by setting (x + -0.2727272728) equal to 1.199173269 and -1.199173269.Subproblem 1
x + -0.2727272728 = 1.199173269 Simplifying x + -0.2727272728 = 1.199173269 Reorder the terms: -0.2727272728 + x = 1.199173269 Solving -0.2727272728 + x = 1.199173269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = 1.199173269 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = 1.199173269 + 0.2727272728 x = 1.199173269 + 0.2727272728 Combine like terms: 1.199173269 + 0.2727272728 = 1.4719005418 x = 1.4719005418 Simplifying x = 1.4719005418Subproblem 2
x + -0.2727272728 = -1.199173269 Simplifying x + -0.2727272728 = -1.199173269 Reorder the terms: -0.2727272728 + x = -1.199173269 Solving -0.2727272728 + x = -1.199173269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = -1.199173269 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = -1.199173269 + 0.2727272728 x = -1.199173269 + 0.2727272728 Combine like terms: -1.199173269 + 0.2727272728 = -0.9264459962 x = -0.9264459962 Simplifying x = -0.9264459962Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4719005418, -0.9264459962}
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