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Simplifying x2 + 40 + 10x + 35 = 180 Reorder the terms: 40 + 35 + 10x + x2 = 180 Combine like terms: 40 + 35 = 75 75 + 10x + x2 = 180 Solving 75 + 10x + x2 = 180 Solving for variable 'x'. Reorder the terms: 75 + -180 + 10x + x2 = 180 + -180 Combine like terms: 75 + -180 = -105 -105 + 10x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -105 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + 10x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + 10x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + 10x + x2 = 0 + 105 10x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 10x + x2 = 105 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 105 + 25 Reorder the terms: 25 + 10x + x2 = 105 + 25 Combine like terms: 105 + 25 = 130 25 + 10x + x2 = 130 Factor a perfect square on the left side: (x + 5)(x + 5) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (x + 5) equal to 11.401754251 and -11.401754251.Subproblem 1
x + 5 = 11.401754251 Simplifying x + 5 = 11.401754251 Reorder the terms: 5 + x = 11.401754251 Solving 5 + x = 11.401754251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 11.401754251 + -5 Combine like terms: 5 + -5 = 0 0 + x = 11.401754251 + -5 x = 11.401754251 + -5 Combine like terms: 11.401754251 + -5 = 6.401754251 x = 6.401754251 Simplifying x = 6.401754251Subproblem 2
x + 5 = -11.401754251 Simplifying x + 5 = -11.401754251 Reorder the terms: 5 + x = -11.401754251 Solving 5 + x = -11.401754251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -11.401754251 + -5 Combine like terms: 5 + -5 = 0 0 + x = -11.401754251 + -5 x = -11.401754251 + -5 Combine like terms: -11.401754251 + -5 = -16.401754251 x = -16.401754251 Simplifying x = -16.401754251Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.401754251, -16.401754251}
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