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Simplifying (13x2 + 5x) + -2(x2 + 1) = 0 Reorder the terms: (5x + 13x2) + -2(x2 + 1) = 0 Remove parenthesis around (5x + 13x2) 5x + 13x2 + -2(x2 + 1) = 0 Reorder the terms: 5x + 13x2 + -2(1 + x2) = 0 5x + 13x2 + (1 * -2 + x2 * -2) = 0 5x + 13x2 + (-2 + -2x2) = 0 Reorder the terms: -2 + 5x + 13x2 + -2x2 = 0 Combine like terms: 13x2 + -2x2 = 11x2 -2 + 5x + 11x2 = 0 Solving -2 + 5x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.1818181818 + 0.4545454545x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.4545454545x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + 0.4545454545x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + 0.4545454545x + x2 = 0 + 0.1818181818 0.4545454545x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 0.4545454545x + x2 = 0.1818181818 The x term is 0.4545454545x. Take half its coefficient (0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. 0.4545454545x + 0.05165289257 + x2 = 0.1818181818 + 0.05165289257 Reorder the terms: 0.05165289257 + 0.4545454545x + x2 = 0.1818181818 + 0.05165289257 Combine like terms: 0.1818181818 + 0.05165289257 = 0.23347107437 0.05165289257 + 0.4545454545x + x2 = 0.23347107437 Factor a perfect square on the left side: (x + 0.2272727273)(x + 0.2272727273) = 0.23347107437 Calculate the square root of the right side: 0.483188446 Break this problem into two subproblems by setting (x + 0.2272727273) equal to 0.483188446 and -0.483188446.Subproblem 1
x + 0.2272727273 = 0.483188446 Simplifying x + 0.2272727273 = 0.483188446 Reorder the terms: 0.2272727273 + x = 0.483188446 Solving 0.2272727273 + x = 0.483188446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = 0.483188446 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = 0.483188446 + -0.2272727273 x = 0.483188446 + -0.2272727273 Combine like terms: 0.483188446 + -0.2272727273 = 0.2559157187 x = 0.2559157187 Simplifying x = 0.2559157187Subproblem 2
x + 0.2272727273 = -0.483188446 Simplifying x + 0.2272727273 = -0.483188446 Reorder the terms: 0.2272727273 + x = -0.483188446 Solving 0.2272727273 + x = -0.483188446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = -0.483188446 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = -0.483188446 + -0.2272727273 x = -0.483188446 + -0.2272727273 Combine like terms: -0.483188446 + -0.2272727273 = -0.7104611733 x = -0.7104611733 Simplifying x = -0.7104611733Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2559157187, -0.7104611733}
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