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Simplifying (x + 3 + 5) * x + 3 = 75 Reorder the terms: (3 + 5 + x) * x + 3 = 75 Combine like terms: 3 + 5 = 8 (8 + x) * x + 3 = 75 Reorder the terms for easier multiplication: x(8 + x) + 3 = 75 (8 * x + x * x) + 3 = 75 (8x + x2) + 3 = 75 Reorder the terms: 3 + 8x + x2 = 75 Solving 3 + 8x + x2 = 75 Solving for variable 'x'. Reorder the terms: 3 + -75 + 8x + x2 = 75 + -75 Combine like terms: 3 + -75 = -72 -72 + 8x + x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -72 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 8x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 8x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 8x + x2 = 0 + 72 8x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 8x + x2 = 72 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 = 72 + 16 Reorder the terms: 16 + 8x + x2 = 72 + 16 Combine like terms: 72 + 16 = 88 16 + 8x + x2 = 88 Factor a perfect square on the left side: (x + 4)(x + 4) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + 4) equal to 9.38083152 and -9.38083152.Subproblem 1
x + 4 = 9.38083152 Simplifying x + 4 = 9.38083152 Reorder the terms: 4 + x = 9.38083152 Solving 4 + x = 9.38083152 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 = 9.38083152 + -4 Combine like terms: 4 + -4 = 0 0 + x = 9.38083152 + -4 x = 9.38083152 + -4 Combine like terms: 9.38083152 + -4 = 5.38083152 x = 5.38083152 Simplifying x = 5.38083152Subproblem 2
x + 4 = -9.38083152 Simplifying x + 4 = -9.38083152 Reorder the terms: 4 + x = -9.38083152 Solving 4 + x = -9.38083152 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 = -9.38083152 + -4 Combine like terms: 4 + -4 = 0 0 + x = -9.38083152 + -4 x = -9.38083152 + -4 Combine like terms: -9.38083152 + -4 = -13.38083152 x = -13.38083152 Simplifying x = -13.38083152Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.38083152, -13.38083152}
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