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Simplifying x2 + 5x + -170 = 0 Reorder the terms: -170 + 5x + x2 = 0 Solving -170 + 5x + 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 + 5x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 5x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 5x + x2 = 0 + 170 5x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 5x + x2 = 170 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 = 170 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 170 + 6.25 Combine like terms: 170 + 6.25 = 176.25 6.25 + 5x + x2 = 176.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 176.25 Calculate the square root of the right side: 13.275918047 Break this problem into two subproblems by setting (x + 2.5) equal to 13.275918047 and -13.275918047.Subproblem 1
x + 2.5 = 13.275918047 Simplifying x + 2.5 = 13.275918047 Reorder the terms: 2.5 + x = 13.275918047 Solving 2.5 + x = 13.275918047 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 = 13.275918047 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 13.275918047 + -2.5 x = 13.275918047 + -2.5 Combine like terms: 13.275918047 + -2.5 = 10.775918047 x = 10.775918047 Simplifying x = 10.775918047Subproblem 2
x + 2.5 = -13.275918047 Simplifying x + 2.5 = -13.275918047 Reorder the terms: 2.5 + x = -13.275918047 Solving 2.5 + x = -13.275918047 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 = -13.275918047 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -13.275918047 + -2.5 x = -13.275918047 + -2.5 Combine like terms: -13.275918047 + -2.5 = -15.775918047 x = -15.775918047 Simplifying x = -15.775918047Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.775918047, -15.775918047}
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