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Simplifying x(x + 2) + 5 = 315 Reorder the terms: x(2 + x) + 5 = 315 (2 * x + x * x) + 5 = 315 (2x + x2) + 5 = 315 Reorder the terms: 5 + 2x + x2 = 315 Solving 5 + 2x + x2 = 315 Solving for variable 'x'. Reorder the terms: 5 + -315 + 2x + x2 = 315 + -315 Combine like terms: 5 + -315 = -310 -310 + 2x + x2 = 315 + -315 Combine like terms: 315 + -315 = 0 -310 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '310' to each side of the equation. -310 + 2x + 310 + x2 = 0 + 310 Reorder the terms: -310 + 310 + 2x + x2 = 0 + 310 Combine like terms: -310 + 310 = 0 0 + 2x + x2 = 0 + 310 2x + x2 = 0 + 310 Combine like terms: 0 + 310 = 310 2x + x2 = 310 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 = 310 + 1 Reorder the terms: 1 + 2x + x2 = 310 + 1 Combine like terms: 310 + 1 = 311 1 + 2x + x2 = 311 Factor a perfect square on the left side: (x + 1)(x + 1) = 311 Calculate the square root of the right side: 17.635192089 Break this problem into two subproblems by setting (x + 1) equal to 17.635192089 and -17.635192089.Subproblem 1
x + 1 = 17.635192089 Simplifying x + 1 = 17.635192089 Reorder the terms: 1 + x = 17.635192089 Solving 1 + x = 17.635192089 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 = 17.635192089 + -1 Combine like terms: 1 + -1 = 0 0 + x = 17.635192089 + -1 x = 17.635192089 + -1 Combine like terms: 17.635192089 + -1 = 16.635192089 x = 16.635192089 Simplifying x = 16.635192089Subproblem 2
x + 1 = -17.635192089 Simplifying x + 1 = -17.635192089 Reorder the terms: 1 + x = -17.635192089 Solving 1 + x = -17.635192089 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 = -17.635192089 + -1 Combine like terms: 1 + -1 = 0 0 + x = -17.635192089 + -1 x = -17.635192089 + -1 Combine like terms: -17.635192089 + -1 = -18.635192089 x = -18.635192089 Simplifying x = -18.635192089Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.635192089, -18.635192089}
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