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Simplifying -3x + 5 = x2 + x + -6 Reorder the terms: 5 + -3x = x2 + x + -6 Reorder the terms: 5 + -3x = -6 + x + x2 Solving 5 + -3x = -6 + x + x2 Solving for variable 'x'. Reorder the terms: 5 + 6 + -3x + -1x + -1x2 = -6 + x + x2 + 6 + -1x + -1x2 Combine like terms: 5 + 6 = 11 11 + -3x + -1x + -1x2 = -6 + x + x2 + 6 + -1x + -1x2 Combine like terms: -3x + -1x = -4x 11 + -4x + -1x2 = -6 + x + x2 + 6 + -1x + -1x2 Reorder the terms: 11 + -4x + -1x2 = -6 + 6 + x + -1x + x2 + -1x2 Combine like terms: -6 + 6 = 0 11 + -4x + -1x2 = 0 + x + -1x + x2 + -1x2 11 + -4x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 11 + -4x + -1x2 = 0 + x2 + -1x2 11 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 11 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + 4x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 4x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 4x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 4x + x2 = 0 + 11 4x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 4x + x2 = 11 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 11 + 4 Reorder the terms: 4 + 4x + x2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + 4x + x2 = 15 Factor a perfect square on the left side: (x + 2)(x + 2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 2) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 2 = 3.872983346 Simplifying x + 2 = 3.872983346 Reorder the terms: 2 + x = 3.872983346 Solving 2 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.872983346 + -2 x = 3.872983346 + -2 Combine like terms: 3.872983346 + -2 = 1.872983346 x = 1.872983346 Simplifying x = 1.872983346Subproblem 2
x + 2 = -3.872983346 Simplifying x + 2 = -3.872983346 Reorder the terms: 2 + x = -3.872983346 Solving 2 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.872983346 + -2 x = -3.872983346 + -2 Combine like terms: -3.872983346 + -2 = -5.872983346 x = -5.872983346 Simplifying x = -5.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.872983346, -5.872983346}
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