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Simplifying x2 + 35x + -1285 = 0 Reorder the terms: -1285 + 35x + x2 = 0 Solving -1285 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1285' to each side of the equation. -1285 + 35x + 1285 + x2 = 0 + 1285 Reorder the terms: -1285 + 1285 + 35x + x2 = 0 + 1285 Combine like terms: -1285 + 1285 = 0 0 + 35x + x2 = 0 + 1285 35x + x2 = 0 + 1285 Combine like terms: 0 + 1285 = 1285 35x + x2 = 1285 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = 1285 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 1285 + 306.25 Combine like terms: 1285 + 306.25 = 1591.25 306.25 + 35x + x2 = 1591.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 1591.25 Calculate the square root of the right side: 39.890475054 Break this problem into two subproblems by setting (x + 17.5) equal to 39.890475054 and -39.890475054.Subproblem 1
x + 17.5 = 39.890475054 Simplifying x + 17.5 = 39.890475054 Reorder the terms: 17.5 + x = 39.890475054 Solving 17.5 + x = 39.890475054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 39.890475054 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 39.890475054 + -17.5 x = 39.890475054 + -17.5 Combine like terms: 39.890475054 + -17.5 = 22.390475054 x = 22.390475054 Simplifying x = 22.390475054Subproblem 2
x + 17.5 = -39.890475054 Simplifying x + 17.5 = -39.890475054 Reorder the terms: 17.5 + x = -39.890475054 Solving 17.5 + x = -39.890475054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -39.890475054 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -39.890475054 + -17.5 x = -39.890475054 + -17.5 Combine like terms: -39.890475054 + -17.5 = -57.390475054 x = -57.390475054 Simplifying x = -57.390475054Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.390475054, -57.390475054}
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