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Simplifying x(x + 2) = 782 Reorder the terms: x(2 + x) = 782 (2 * x + x * x) = 782 (2x + x2) = 782 Solving 2x + x2 = 782 Solving for variable 'x'. Reorder the terms: -782 + 2x + x2 = 782 + -782 Combine like terms: 782 + -782 = 0 -782 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '782' to each side of the equation. -782 + 2x + 782 + x2 = 0 + 782 Reorder the terms: -782 + 782 + 2x + x2 = 0 + 782 Combine like terms: -782 + 782 = 0 0 + 2x + x2 = 0 + 782 2x + x2 = 0 + 782 Combine like terms: 0 + 782 = 782 2x + x2 = 782 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 782 + 1 Reorder the terms: 1 + 2x + x2 = 782 + 1 Combine like terms: 782 + 1 = 783 1 + 2x + x2 = 783 Factor a perfect square on the left side: (x + 1)(x + 1) = 783 Calculate the square root of the right side: 27.982137159 Break this problem into two subproblems by setting (x + 1) equal to 27.982137159 and -27.982137159.Subproblem 1
x + 1 = 27.982137159 Simplifying x + 1 = 27.982137159 Reorder the terms: 1 + x = 27.982137159 Solving 1 + x = 27.982137159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 27.982137159 + -1 Combine like terms: 1 + -1 = 0 0 + x = 27.982137159 + -1 x = 27.982137159 + -1 Combine like terms: 27.982137159 + -1 = 26.982137159 x = 26.982137159 Simplifying x = 26.982137159Subproblem 2
x + 1 = -27.982137159 Simplifying x + 1 = -27.982137159 Reorder the terms: 1 + x = -27.982137159 Solving 1 + x = -27.982137159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -27.982137159 + -1 Combine like terms: 1 + -1 = 0 0 + x = -27.982137159 + -1 x = -27.982137159 + -1 Combine like terms: -27.982137159 + -1 = -28.982137159 x = -28.982137159 Simplifying x = -28.982137159Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.982137159, -28.982137159}
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