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Simplifying (x + -3)(x + 3) + 11 = 8x Reorder the terms: (-3 + x)(x + 3) + 11 = 8x Reorder the terms: (-3 + x)(3 + x) + 11 = 8x Multiply (-3 + x) * (3 + x) (-3(3 + x) + x(3 + x)) + 11 = 8x ((3 * -3 + x * -3) + x(3 + x)) + 11 = 8x ((-9 + -3x) + x(3 + x)) + 11 = 8x (-9 + -3x + (3 * x + x * x)) + 11 = 8x (-9 + -3x + (3x + x2)) + 11 = 8x Combine like terms: -3x + 3x = 0 (-9 + 0 + x2) + 11 = 8x (-9 + x2) + 11 = 8x Reorder the terms: -9 + 11 + x2 = 8x Combine like terms: -9 + 11 = 2 2 + x2 = 8x Solving 2 + x2 = 8x Solving for variable 'x'. Reorder the terms: 2 + -8x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 2 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -8x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -8x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -8x + x2 = 0 + -2 -8x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -8x + x2 = -2 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -2 + 16 Reorder the terms: 16 + -8x + x2 = -2 + 16 Combine like terms: -2 + 16 = 14 16 + -8x + x2 = 14 Factor a perfect square on the left side: (x + -4)(x + -4) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -4) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -4 = 3.741657387 Simplifying x + -4 = 3.741657387 Reorder the terms: -4 + x = 3.741657387 Solving -4 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.741657387 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.741657387 + 4 x = 3.741657387 + 4 Combine like terms: 3.741657387 + 4 = 7.741657387 x = 7.741657387 Simplifying x = 7.741657387Subproblem 2
x + -4 = -3.741657387 Simplifying x + -4 = -3.741657387 Reorder the terms: -4 + x = -3.741657387 Solving -4 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.741657387 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.741657387 + 4 x = -3.741657387 + 4 Combine like terms: -3.741657387 + 4 = 0.258342613 x = 0.258342613 Simplifying x = 0.258342613Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.741657387, 0.258342613}
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