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Simplifying x(x + 32) = 7 Reorder the terms: x(32 + x) = 7 (32 * x + x * x) = 7 (32x + x2) = 7 Solving 32x + x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 32x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 32x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 32x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 32x + x2 = 0 + 7 32x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 32x + x2 = 7 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 7 + 256 Reorder the terms: 256 + 32x + x2 = 7 + 256 Combine like terms: 7 + 256 = 263 256 + 32x + x2 = 263 Factor a perfect square on the left side: (x + 16)(x + 16) = 263 Calculate the square root of the right side: 16.21727474 Break this problem into two subproblems by setting (x + 16) equal to 16.21727474 and -16.21727474.Subproblem 1
x + 16 = 16.21727474 Simplifying x + 16 = 16.21727474 Reorder the terms: 16 + x = 16.21727474 Solving 16 + x = 16.21727474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 16.21727474 + -16 Combine like terms: 16 + -16 = 0 0 + x = 16.21727474 + -16 x = 16.21727474 + -16 Combine like terms: 16.21727474 + -16 = 0.21727474 x = 0.21727474 Simplifying x = 0.21727474Subproblem 2
x + 16 = -16.21727474 Simplifying x + 16 = -16.21727474 Reorder the terms: 16 + x = -16.21727474 Solving 16 + x = -16.21727474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -16.21727474 + -16 Combine like terms: 16 + -16 = 0 0 + x = -16.21727474 + -16 x = -16.21727474 + -16 Combine like terms: -16.21727474 + -16 = -32.21727474 x = -32.21727474 Simplifying x = -32.21727474Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.21727474, -32.21727474}
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