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Simplifying x + 2x2 = 26.2 Solving x + 2x2 = 26.2 Solving for variable 'x'. Reorder the terms: -26.2 + x + 2x2 = 26.2 + -26.2 Combine like terms: 26.2 + -26.2 = 0.0 -26.2 + x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.1 + 0.5x + x2 = 0.0 Move the constant term to the right: Add '13.1' to each side of the equation. -13.1 + 0.5x + 13.1 + x2 = 0.0 + 13.1 Reorder the terms: -13.1 + 13.1 + 0.5x + x2 = 0.0 + 13.1 Combine like terms: -13.1 + 13.1 = 0.0 0.0 + 0.5x + x2 = 0.0 + 13.1 0.5x + x2 = 0.0 + 13.1 Combine like terms: 0.0 + 13.1 = 13.1 0.5x + x2 = 13.1 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 13.1 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 13.1 + 0.25 Combine like terms: 13.1 + 0.25 = 13.35 0.25 + 0.5x + x2 = 13.35 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 13.35 Calculate the square root of the right side: 3.653765181 Break this problem into two subproblems by setting (x + 0.5) equal to 3.653765181 and -3.653765181.Subproblem 1
x + 0.5 = 3.653765181 Simplifying x + 0.5 = 3.653765181 Reorder the terms: 0.5 + x = 3.653765181 Solving 0.5 + x = 3.653765181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.653765181 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.653765181 + -0.5 x = 3.653765181 + -0.5 Combine like terms: 3.653765181 + -0.5 = 3.153765181 x = 3.153765181 Simplifying x = 3.153765181Subproblem 2
x + 0.5 = -3.653765181 Simplifying x + 0.5 = -3.653765181 Reorder the terms: 0.5 + x = -3.653765181 Solving 0.5 + x = -3.653765181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.653765181 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.653765181 + -0.5 x = -3.653765181 + -0.5 Combine like terms: -3.653765181 + -0.5 = -4.153765181 x = -4.153765181 Simplifying x = -4.153765181Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.153765181, -4.153765181}
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