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Simplifying (x + 8)(x) = 52 Reorder the terms: (8 + x)(x) = 52 Reorder the terms for easier multiplication: x(8 + x) = 52 (8 * x + x * x) = 52 (8x + x2) = 52 Solving 8x + x2 = 52 Solving for variable 'x'. Reorder the terms: -52 + 8x + x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 8x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 8x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 8x + x2 = 0 + 52 8x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 8x + x2 = 52 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 = 52 + 16 Reorder the terms: 16 + 8x + x2 = 52 + 16 Combine like terms: 52 + 16 = 68 16 + 8x + x2 = 68 Factor a perfect square on the left side: (x + 4)(x + 4) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (x + 4) equal to 8.246211251 and -8.246211251.Subproblem 1
x + 4 = 8.246211251 Simplifying x + 4 = 8.246211251 Reorder the terms: 4 + x = 8.246211251 Solving 4 + x = 8.246211251 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 = 8.246211251 + -4 Combine like terms: 4 + -4 = 0 0 + x = 8.246211251 + -4 x = 8.246211251 + -4 Combine like terms: 8.246211251 + -4 = 4.246211251 x = 4.246211251 Simplifying x = 4.246211251Subproblem 2
x + 4 = -8.246211251 Simplifying x + 4 = -8.246211251 Reorder the terms: 4 + x = -8.246211251 Solving 4 + x = -8.246211251 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 = -8.246211251 + -4 Combine like terms: 4 + -4 = 0 0 + x = -8.246211251 + -4 x = -8.246211251 + -4 Combine like terms: -8.246211251 + -4 = -12.246211251 x = -12.246211251 Simplifying x = -12.246211251Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.246211251, -12.246211251}
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