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Simplifying x2 + x + -1 + 11x = 7x + 3 Reorder the terms: -1 + x + 11x + x2 = 7x + 3 Combine like terms: x + 11x = 12x -1 + 12x + x2 = 7x + 3 Reorder the terms: -1 + 12x + x2 = 3 + 7x Solving -1 + 12x + x2 = 3 + 7x Solving for variable 'x'. Reorder the terms: -1 + -3 + 12x + -7x + x2 = 3 + 7x + -3 + -7x Combine like terms: -1 + -3 = -4 -4 + 12x + -7x + x2 = 3 + 7x + -3 + -7x Combine like terms: 12x + -7x = 5x -4 + 5x + x2 = 3 + 7x + -3 + -7x Reorder the terms: -4 + 5x + x2 = 3 + -3 + 7x + -7x Combine like terms: 3 + -3 = 0 -4 + 5x + x2 = 0 + 7x + -7x -4 + 5x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -4 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5x + x2 = 0 + 4 5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 5x + x2 = 4 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 4 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + 5x + x2 = 10.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + 2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + 2.5 = 3.201562119 Simplifying x + 2.5 = 3.201562119 Reorder the terms: 2.5 + x = 3.201562119 Solving 2.5 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.201562119 + -2.5 x = 3.201562119 + -2.5 Combine like terms: 3.201562119 + -2.5 = 0.701562119 x = 0.701562119 Simplifying x = 0.701562119Subproblem 2
x + 2.5 = -3.201562119 Simplifying x + 2.5 = -3.201562119 Reorder the terms: 2.5 + x = -3.201562119 Solving 2.5 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.201562119 + -2.5 x = -3.201562119 + -2.5 Combine like terms: -3.201562119 + -2.5 = -5.701562119 x = -5.701562119 Simplifying x = -5.701562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.701562119, -5.701562119}
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