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Simplifying x2 + 59x + -400 = 0 Reorder the terms: -400 + 59x + x2 = 0 Solving -400 + 59x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 59x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 59x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 59x + x2 = 0 + 400 59x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 59x + x2 = 400 The x term is 59x. Take half its coefficient (29.5). Square it (870.25) and add it to both sides. Add '870.25' to each side of the equation. 59x + 870.25 + x2 = 400 + 870.25 Reorder the terms: 870.25 + 59x + x2 = 400 + 870.25 Combine like terms: 400 + 870.25 = 1270.25 870.25 + 59x + x2 = 1270.25 Factor a perfect square on the left side: (x + 29.5)(x + 29.5) = 1270.25 Calculate the square root of the right side: 35.640566774 Break this problem into two subproblems by setting (x + 29.5) equal to 35.640566774 and -35.640566774.Subproblem 1
x + 29.5 = 35.640566774 Simplifying x + 29.5 = 35.640566774 Reorder the terms: 29.5 + x = 35.640566774 Solving 29.5 + x = 35.640566774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29.5' to each side of the equation. 29.5 + -29.5 + x = 35.640566774 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + x = 35.640566774 + -29.5 x = 35.640566774 + -29.5 Combine like terms: 35.640566774 + -29.5 = 6.140566774 x = 6.140566774 Simplifying x = 6.140566774Subproblem 2
x + 29.5 = -35.640566774 Simplifying x + 29.5 = -35.640566774 Reorder the terms: 29.5 + x = -35.640566774 Solving 29.5 + x = -35.640566774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29.5' to each side of the equation. 29.5 + -29.5 + x = -35.640566774 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + x = -35.640566774 + -29.5 x = -35.640566774 + -29.5 Combine like terms: -35.640566774 + -29.5 = -65.140566774 x = -65.140566774 Simplifying x = -65.140566774Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.140566774, -65.140566774}
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