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Simplifying x2 + 2x + -15 = 270 Reorder the terms: -15 + 2x + x2 = 270 Solving -15 + 2x + x2 = 270 Solving for variable 'x'. Reorder the terms: -15 + -270 + 2x + x2 = 270 + -270 Combine like terms: -15 + -270 = -285 -285 + 2x + x2 = 270 + -270 Combine like terms: 270 + -270 = 0 -285 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '285' to each side of the equation. -285 + 2x + 285 + x2 = 0 + 285 Reorder the terms: -285 + 285 + 2x + x2 = 0 + 285 Combine like terms: -285 + 285 = 0 0 + 2x + x2 = 0 + 285 2x + x2 = 0 + 285 Combine like terms: 0 + 285 = 285 2x + x2 = 285 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 = 285 + 1 Reorder the terms: 1 + 2x + x2 = 285 + 1 Combine like terms: 285 + 1 = 286 1 + 2x + x2 = 286 Factor a perfect square on the left side: (x + 1)(x + 1) = 286 Calculate the square root of the right side: 16.911534525 Break this problem into two subproblems by setting (x + 1) equal to 16.911534525 and -16.911534525.Subproblem 1
x + 1 = 16.911534525 Simplifying x + 1 = 16.911534525 Reorder the terms: 1 + x = 16.911534525 Solving 1 + x = 16.911534525 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 = 16.911534525 + -1 Combine like terms: 1 + -1 = 0 0 + x = 16.911534525 + -1 x = 16.911534525 + -1 Combine like terms: 16.911534525 + -1 = 15.911534525 x = 15.911534525 Simplifying x = 15.911534525Subproblem 2
x + 1 = -16.911534525 Simplifying x + 1 = -16.911534525 Reorder the terms: 1 + x = -16.911534525 Solving 1 + x = -16.911534525 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 = -16.911534525 + -1 Combine like terms: 1 + -1 = 0 0 + x = -16.911534525 + -1 x = -16.911534525 + -1 Combine like terms: -16.911534525 + -1 = -17.911534525 x = -17.911534525 Simplifying x = -17.911534525Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.911534525, -17.911534525}
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