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Simplifying x2 + 2x = 26.01 Reorder the terms: 2x + x2 = 26.01 Solving 2x + x2 = 26.01 Solving for variable 'x'. Reorder the terms: -26.01 + 2x + x2 = 26.01 + -26.01 Combine like terms: 26.01 + -26.01 = 0.00 -26.01 + 2x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '26.01' to each side of the equation. -26.01 + 2x + 26.01 + x2 = 0.00 + 26.01 Reorder the terms: -26.01 + 26.01 + 2x + x2 = 0.00 + 26.01 Combine like terms: -26.01 + 26.01 = 0.00 0.00 + 2x + x2 = 0.00 + 26.01 2x + x2 = 0.00 + 26.01 Combine like terms: 0.00 + 26.01 = 26.01 2x + x2 = 26.01 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 = 26.01 + 1 Reorder the terms: 1 + 2x + x2 = 26.01 + 1 Combine like terms: 26.01 + 1 = 27.01 1 + 2x + x2 = 27.01 Factor a perfect square on the left side: (x + 1)(x + 1) = 27.01 Calculate the square root of the right side: 5.197114584 Break this problem into two subproblems by setting (x + 1) equal to 5.197114584 and -5.197114584.Subproblem 1
x + 1 = 5.197114584 Simplifying x + 1 = 5.197114584 Reorder the terms: 1 + x = 5.197114584 Solving 1 + x = 5.197114584 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 = 5.197114584 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.197114584 + -1 x = 5.197114584 + -1 Combine like terms: 5.197114584 + -1 = 4.197114584 x = 4.197114584 Simplifying x = 4.197114584Subproblem 2
x + 1 = -5.197114584 Simplifying x + 1 = -5.197114584 Reorder the terms: 1 + x = -5.197114584 Solving 1 + x = -5.197114584 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 = -5.197114584 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.197114584 + -1 x = -5.197114584 + -1 Combine like terms: -5.197114584 + -1 = -6.197114584 x = -6.197114584 Simplifying x = -6.197114584Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.197114584, -6.197114584}
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