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Simplifying x(x + 10) = 880 Reorder the terms: x(10 + x) = 880 (10 * x + x * x) = 880 (10x + x2) = 880 Solving 10x + x2 = 880 Solving for variable 'x'. Reorder the terms: -880 + 10x + x2 = 880 + -880 Combine like terms: 880 + -880 = 0 -880 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '880' to each side of the equation. -880 + 10x + 880 + x2 = 0 + 880 Reorder the terms: -880 + 880 + 10x + x2 = 0 + 880 Combine like terms: -880 + 880 = 0 0 + 10x + x2 = 0 + 880 10x + x2 = 0 + 880 Combine like terms: 0 + 880 = 880 10x + x2 = 880 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 = 880 + 25 Reorder the terms: 25 + 10x + x2 = 880 + 25 Combine like terms: 880 + 25 = 905 25 + 10x + x2 = 905 Factor a perfect square on the left side: (x + 5)(x + 5) = 905 Calculate the square root of the right side: 30.083217913 Break this problem into two subproblems by setting (x + 5) equal to 30.083217913 and -30.083217913.Subproblem 1
x + 5 = 30.083217913 Simplifying x + 5 = 30.083217913 Reorder the terms: 5 + x = 30.083217913 Solving 5 + x = 30.083217913 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 = 30.083217913 + -5 Combine like terms: 5 + -5 = 0 0 + x = 30.083217913 + -5 x = 30.083217913 + -5 Combine like terms: 30.083217913 + -5 = 25.083217913 x = 25.083217913 Simplifying x = 25.083217913Subproblem 2
x + 5 = -30.083217913 Simplifying x + 5 = -30.083217913 Reorder the terms: 5 + x = -30.083217913 Solving 5 + x = -30.083217913 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 = -30.083217913 + -5 Combine like terms: 5 + -5 = 0 0 + x = -30.083217913 + -5 x = -30.083217913 + -5 Combine like terms: -30.083217913 + -5 = -35.083217913 x = -35.083217913 Simplifying x = -35.083217913Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.083217913, -35.083217913}
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