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Simplifying x2 + 5x + -520 = 0 Reorder the terms: -520 + 5x + x2 = 0 Solving -520 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '520' to each side of the equation. -520 + 5x + 520 + x2 = 0 + 520 Reorder the terms: -520 + 520 + 5x + x2 = 0 + 520 Combine like terms: -520 + 520 = 0 0 + 5x + x2 = 0 + 520 5x + x2 = 0 + 520 Combine like terms: 0 + 520 = 520 5x + x2 = 520 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 520 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 520 + 6.25 Combine like terms: 520 + 6.25 = 526.25 6.25 + 5x + x2 = 526.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 526.25 Calculate the square root of the right side: 22.940139494 Break this problem into two subproblems by setting (x + 2.5) equal to 22.940139494 and -22.940139494.Subproblem 1
x + 2.5 = 22.940139494 Simplifying x + 2.5 = 22.940139494 Reorder the terms: 2.5 + x = 22.940139494 Solving 2.5 + x = 22.940139494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 22.940139494 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 22.940139494 + -2.5 x = 22.940139494 + -2.5 Combine like terms: 22.940139494 + -2.5 = 20.440139494 x = 20.440139494 Simplifying x = 20.440139494Subproblem 2
x + 2.5 = -22.940139494 Simplifying x + 2.5 = -22.940139494 Reorder the terms: 2.5 + x = -22.940139494 Solving 2.5 + x = -22.940139494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -22.940139494 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -22.940139494 + -2.5 x = -22.940139494 + -2.5 Combine like terms: -22.940139494 + -2.5 = -25.440139494 x = -25.440139494 Simplifying x = -25.440139494Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.440139494, -25.440139494}
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