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Simplifying (x)(x + 2) = 284 Reorder the terms: x(2 + x) = 284 (2 * x + x * x) = 284 (2x + x2) = 284 Solving 2x + x2 = 284 Solving for variable 'x'. Reorder the terms: -284 + 2x + x2 = 284 + -284 Combine like terms: 284 + -284 = 0 -284 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '284' to each side of the equation. -284 + 2x + 284 + x2 = 0 + 284 Reorder the terms: -284 + 284 + 2x + x2 = 0 + 284 Combine like terms: -284 + 284 = 0 0 + 2x + x2 = 0 + 284 2x + x2 = 0 + 284 Combine like terms: 0 + 284 = 284 2x + x2 = 284 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 = 284 + 1 Reorder the terms: 1 + 2x + x2 = 284 + 1 Combine like terms: 284 + 1 = 285 1 + 2x + x2 = 285 Factor a perfect square on the left side: (x + 1)(x + 1) = 285 Calculate the square root of the right side: 16.881943016 Break this problem into two subproblems by setting (x + 1) equal to 16.881943016 and -16.881943016.Subproblem 1
x + 1 = 16.881943016 Simplifying x + 1 = 16.881943016 Reorder the terms: 1 + x = 16.881943016 Solving 1 + x = 16.881943016 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 = 16.881943016 + -1 Combine like terms: 1 + -1 = 0 0 + x = 16.881943016 + -1 x = 16.881943016 + -1 Combine like terms: 16.881943016 + -1 = 15.881943016 x = 15.881943016 Simplifying x = 15.881943016Subproblem 2
x + 1 = -16.881943016 Simplifying x + 1 = -16.881943016 Reorder the terms: 1 + x = -16.881943016 Solving 1 + x = -16.881943016 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 = -16.881943016 + -1 Combine like terms: 1 + -1 = 0 0 + x = -16.881943016 + -1 x = -16.881943016 + -1 Combine like terms: -16.881943016 + -1 = -17.881943016 x = -17.881943016 Simplifying x = -17.881943016Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.881943016, -17.881943016}
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