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Simplifying x(x + 8) = (x + 4) Reorder the terms: x(8 + x) = (x + 4) (8 * x + x * x) = (x + 4) (8x + x2) = (x + 4) Reorder the terms: 8x + x2 = (4 + x) Remove parenthesis around (4 + x) 8x + x2 = 4 + x Solving 8x + x2 = 4 + x Solving for variable 'x'. Reorder the terms: -4 + 8x + -1x + x2 = 4 + x + -4 + -1x Combine like terms: 8x + -1x = 7x -4 + 7x + x2 = 4 + x + -4 + -1x Reorder the terms: -4 + 7x + x2 = 4 + -4 + x + -1x Combine like terms: 4 + -4 = 0 -4 + 7x + x2 = 0 + x + -1x -4 + 7x + x2 = x + -1x Combine like terms: x + -1x = 0 -4 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 7x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 7x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7x + x2 = 0 + 4 7x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 7x + x2 = 4 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 4 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 4 + 12.25 Combine like terms: 4 + 12.25 = 16.25 12.25 + 7x + x2 = 16.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + 3.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + 3.5 = 4.031128874 Simplifying x + 3.5 = 4.031128874 Reorder the terms: 3.5 + x = 4.031128874 Solving 3.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.031128874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.031128874 + -3.5 x = 4.031128874 + -3.5 Combine like terms: 4.031128874 + -3.5 = 0.531128874 x = 0.531128874 Simplifying x = 0.531128874Subproblem 2
x + 3.5 = -4.031128874 Simplifying x + 3.5 = -4.031128874 Reorder the terms: 3.5 + x = -4.031128874 Solving 3.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.031128874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.031128874 + -3.5 x = -4.031128874 + -3.5 Combine like terms: -4.031128874 + -3.5 = -7.531128874 x = -7.531128874 Simplifying x = -7.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.531128874, -7.531128874}
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