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Simplifying x(x + 10) = 161 Reorder the terms: x(10 + x) = 161 (10 * x + x * x) = 161 (10x + x2) = 161 Solving 10x + x2 = 161 Solving for variable 'x'. Reorder the terms: -161 + 10x + x2 = 161 + -161 Combine like terms: 161 + -161 = 0 -161 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '161' to each side of the equation. -161 + 10x + 161 + x2 = 0 + 161 Reorder the terms: -161 + 161 + 10x + x2 = 0 + 161 Combine like terms: -161 + 161 = 0 0 + 10x + x2 = 0 + 161 10x + x2 = 0 + 161 Combine like terms: 0 + 161 = 161 10x + x2 = 161 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 = 161 + 25 Reorder the terms: 25 + 10x + x2 = 161 + 25 Combine like terms: 161 + 25 = 186 25 + 10x + x2 = 186 Factor a perfect square on the left side: (x + 5)(x + 5) = 186 Calculate the square root of the right side: 13.638181697 Break this problem into two subproblems by setting (x + 5) equal to 13.638181697 and -13.638181697.Subproblem 1
x + 5 = 13.638181697 Simplifying x + 5 = 13.638181697 Reorder the terms: 5 + x = 13.638181697 Solving 5 + x = 13.638181697 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 = 13.638181697 + -5 Combine like terms: 5 + -5 = 0 0 + x = 13.638181697 + -5 x = 13.638181697 + -5 Combine like terms: 13.638181697 + -5 = 8.638181697 x = 8.638181697 Simplifying x = 8.638181697Subproblem 2
x + 5 = -13.638181697 Simplifying x + 5 = -13.638181697 Reorder the terms: 5 + x = -13.638181697 Solving 5 + x = -13.638181697 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 = -13.638181697 + -5 Combine like terms: 5 + -5 = 0 0 + x = -13.638181697 + -5 x = -13.638181697 + -5 Combine like terms: -13.638181697 + -5 = -18.638181697 x = -18.638181697 Simplifying x = -18.638181697Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.638181697, -18.638181697}
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