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Simplifying x * x + 2x = 115 Multiply x * x x2 + 2x = 115 Reorder the terms: 2x + x2 = 115 Solving 2x + x2 = 115 Solving for variable 'x'. Reorder the terms: -115 + 2x + x2 = 115 + -115 Combine like terms: 115 + -115 = 0 -115 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '115' to each side of the equation. -115 + 2x + 115 + x2 = 0 + 115 Reorder the terms: -115 + 115 + 2x + x2 = 0 + 115 Combine like terms: -115 + 115 = 0 0 + 2x + x2 = 0 + 115 2x + x2 = 0 + 115 Combine like terms: 0 + 115 = 115 2x + x2 = 115 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 115 + 1 Reorder the terms: 1 + 2x + x2 = 115 + 1 Combine like terms: 115 + 1 = 116 1 + 2x + x2 = 116 Factor a perfect square on the left side: (x + 1)(x + 1) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (x + 1) equal to 10.770329614 and -10.770329614.Subproblem 1
x + 1 = 10.770329614 Simplifying x + 1 = 10.770329614 Reorder the terms: 1 + x = 10.770329614 Solving 1 + x = 10.770329614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 10.770329614 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.770329614 + -1 x = 10.770329614 + -1 Combine like terms: 10.770329614 + -1 = 9.770329614 x = 9.770329614 Simplifying x = 9.770329614Subproblem 2
x + 1 = -10.770329614 Simplifying x + 1 = -10.770329614 Reorder the terms: 1 + x = -10.770329614 Solving 1 + x = -10.770329614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -10.770329614 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.770329614 + -1 x = -10.770329614 + -1 Combine like terms: -10.770329614 + -1 = -11.770329614 x = -11.770329614 Simplifying x = -11.770329614Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.770329614, -11.770329614}
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