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Simplifying (x + -3)(x + 3) = (x + 36) Reorder the terms: (-3 + x)(x + 3) = (x + 36) Reorder the terms: (-3 + x)(3 + x) = (x + 36) Multiply (-3 + x) * (3 + x) (-3(3 + x) + x(3 + x)) = (x + 36) ((3 * -3 + x * -3) + x(3 + x)) = (x + 36) ((-9 + -3x) + x(3 + x)) = (x + 36) (-9 + -3x + (3 * x + x * x)) = (x + 36) (-9 + -3x + (3x + x2)) = (x + 36) Combine like terms: -3x + 3x = 0 (-9 + 0 + x2) = (x + 36) (-9 + x2) = (x + 36) Reorder the terms: -9 + x2 = (36 + x) Remove parenthesis around (36 + x) -9 + x2 = 36 + x Solving -9 + x2 = 36 + x Solving for variable 'x'. Reorder the terms: -9 + -36 + -1x + x2 = 36 + x + -36 + -1x Combine like terms: -9 + -36 = -45 -45 + -1x + x2 = 36 + x + -36 + -1x Reorder the terms: -45 + -1x + x2 = 36 + -36 + x + -1x Combine like terms: 36 + -36 = 0 -45 + -1x + x2 = 0 + x + -1x -45 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -45 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -1x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -1x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -1x + x2 = 0 + 45 -1x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -1x + x2 = 45 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 45 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 45 + 0.25 Combine like terms: 45 + 0.25 = 45.25 0.25 + -1x + x2 = 45.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + -0.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + -0.5 = 6.726812024 Simplifying x + -0.5 = 6.726812024 Reorder the terms: -0.5 + x = 6.726812024 Solving -0.5 + x = 6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 6.726812024 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.726812024 + 0.5 x = 6.726812024 + 0.5 Combine like terms: 6.726812024 + 0.5 = 7.226812024 x = 7.226812024 Simplifying x = 7.226812024Subproblem 2
x + -0.5 = -6.726812024 Simplifying x + -0.5 = -6.726812024 Reorder the terms: -0.5 + x = -6.726812024 Solving -0.5 + x = -6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -6.726812024 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.726812024 + 0.5 x = -6.726812024 + 0.5 Combine like terms: -6.726812024 + 0.5 = -6.226812024 x = -6.226812024 Simplifying x = -6.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.226812024, -6.226812024}
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