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Simplifying x2 + x + 0 = 520 Reorder the terms: 0 + x + x2 = 520 Remove the zero: x + x2 = 520 Solving x + x2 = 520 Solving for variable 'x'. Reorder the terms: -520 + x + x2 = 520 + -520 Combine like terms: 520 + -520 = 0 -520 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '520' to each side of the equation. -520 + x + 520 + x2 = 0 + 520 Reorder the terms: -520 + 520 + x + x2 = 0 + 520 Combine like terms: -520 + 520 = 0 0 + x + x2 = 0 + 520 x + x2 = 0 + 520 Combine like terms: 0 + 520 = 520 x + x2 = 520 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 520 + 0.25 Reorder the terms: 0.25 + x + x2 = 520 + 0.25 Combine like terms: 520 + 0.25 = 520.25 0.25 + x + x2 = 520.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 520.25 Calculate the square root of the right side: 22.808989456 Break this problem into two subproblems by setting (x + 0.5) equal to 22.808989456 and -22.808989456.Subproblem 1
x + 0.5 = 22.808989456 Simplifying x + 0.5 = 22.808989456 Reorder the terms: 0.5 + x = 22.808989456 Solving 0.5 + x = 22.808989456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 22.808989456 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 22.808989456 + -0.5 x = 22.808989456 + -0.5 Combine like terms: 22.808989456 + -0.5 = 22.308989456 x = 22.308989456 Simplifying x = 22.308989456Subproblem 2
x + 0.5 = -22.808989456 Simplifying x + 0.5 = -22.808989456 Reorder the terms: 0.5 + x = -22.808989456 Solving 0.5 + x = -22.808989456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -22.808989456 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -22.808989456 + -0.5 x = -22.808989456 + -0.5 Combine like terms: -22.808989456 + -0.5 = -23.308989456 x = -23.308989456 Simplifying x = -23.308989456Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.308989456, -23.308989456}
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