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Simplifying x2 + 2x = 450 Reorder the terms: 2x + x2 = 450 Solving 2x + x2 = 450 Solving for variable 'x'. Reorder the terms: -450 + 2x + x2 = 450 + -450 Combine like terms: 450 + -450 = 0 -450 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '450' to each side of the equation. -450 + 2x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + 2x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 2x + x2 = 0 + 450 2x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 2x + x2 = 450 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 = 450 + 1 Reorder the terms: 1 + 2x + x2 = 450 + 1 Combine like terms: 450 + 1 = 451 1 + 2x + x2 = 451 Factor a perfect square on the left side: (x + 1)(x + 1) = 451 Calculate the square root of the right side: 21.236760582 Break this problem into two subproblems by setting (x + 1) equal to 21.236760582 and -21.236760582.Subproblem 1
x + 1 = 21.236760582 Simplifying x + 1 = 21.236760582 Reorder the terms: 1 + x = 21.236760582 Solving 1 + x = 21.236760582 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 = 21.236760582 + -1 Combine like terms: 1 + -1 = 0 0 + x = 21.236760582 + -1 x = 21.236760582 + -1 Combine like terms: 21.236760582 + -1 = 20.236760582 x = 20.236760582 Simplifying x = 20.236760582Subproblem 2
x + 1 = -21.236760582 Simplifying x + 1 = -21.236760582 Reorder the terms: 1 + x = -21.236760582 Solving 1 + x = -21.236760582 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 = -21.236760582 + -1 Combine like terms: 1 + -1 = 0 0 + x = -21.236760582 + -1 x = -21.236760582 + -1 Combine like terms: -21.236760582 + -1 = -22.236760582 x = -22.236760582 Simplifying x = -22.236760582Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.236760582, -22.236760582}
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