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Simplifying x2 + 59x + -170 = 0 Reorder the terms: -170 + 59x + x2 = 0 Solving -170 + 59x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '170' to each side of the equation. -170 + 59x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 59x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 59x + x2 = 0 + 170 59x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 59x + x2 = 170 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 = 170 + 870.25 Reorder the terms: 870.25 + 59x + x2 = 170 + 870.25 Combine like terms: 170 + 870.25 = 1040.25 870.25 + 59x + x2 = 1040.25 Factor a perfect square on the left side: (x + 29.5)(x + 29.5) = 1040.25 Calculate the square root of the right side: 32.252906846 Break this problem into two subproblems by setting (x + 29.5) equal to 32.252906846 and -32.252906846.Subproblem 1
x + 29.5 = 32.252906846 Simplifying x + 29.5 = 32.252906846 Reorder the terms: 29.5 + x = 32.252906846 Solving 29.5 + x = 32.252906846 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 = 32.252906846 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + x = 32.252906846 + -29.5 x = 32.252906846 + -29.5 Combine like terms: 32.252906846 + -29.5 = 2.752906846 x = 2.752906846 Simplifying x = 2.752906846Subproblem 2
x + 29.5 = -32.252906846 Simplifying x + 29.5 = -32.252906846 Reorder the terms: 29.5 + x = -32.252906846 Solving 29.5 + x = -32.252906846 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 = -32.252906846 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + x = -32.252906846 + -29.5 x = -32.252906846 + -29.5 Combine like terms: -32.252906846 + -29.5 = -61.752906846 x = -61.752906846 Simplifying x = -61.752906846Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.752906846, -61.752906846}
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