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Simplifying 6x * 6x + -21 = 5x * 5x + -4x Reorder the terms for easier multiplication: 6 * 6x * x + -21 = 5x * 5x + -4x Multiply 6 * 6 36x * x + -21 = 5x * 5x + -4x Multiply x * x 36x2 + -21 = 5x * 5x + -4x Reorder the terms: -21 + 36x2 = 5x * 5x + -4x Reorder the terms for easier multiplication: -21 + 36x2 = 5 * 5x * x + -4x Multiply 5 * 5 -21 + 36x2 = 25x * x + -4x Multiply x * x -21 + 36x2 = 25x2 + -4x Reorder the terms: -21 + 36x2 = -4x + 25x2 Solving -21 + 36x2 = -4x + 25x2 Solving for variable 'x'. Reorder the terms: -21 + 4x + 36x2 + -25x2 = -4x + 25x2 + 4x + -25x2 Combine like terms: 36x2 + -25x2 = 11x2 -21 + 4x + 11x2 = -4x + 25x2 + 4x + -25x2 Reorder the terms: -21 + 4x + 11x2 = -4x + 4x + 25x2 + -25x2 Combine like terms: -4x + 4x = 0 -21 + 4x + 11x2 = 0 + 25x2 + -25x2 -21 + 4x + 11x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 -21 + 4x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.909090909 + 0.3636363636x + x2 = 0 Move the constant term to the right: Add '1.909090909' to each side of the equation. -1.909090909 + 0.3636363636x + 1.909090909 + x2 = 0 + 1.909090909 Reorder the terms: -1.909090909 + 1.909090909 + 0.3636363636x + x2 = 0 + 1.909090909 Combine like terms: -1.909090909 + 1.909090909 = 0.000000000 0.000000000 + 0.3636363636x + x2 = 0 + 1.909090909 0.3636363636x + x2 = 0 + 1.909090909 Combine like terms: 0 + 1.909090909 = 1.909090909 0.3636363636x + x2 = 1.909090909 The x term is 0.3636363636x. Take half its coefficient (0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. 0.3636363636x + 0.03305785123 + x2 = 1.909090909 + 0.03305785123 Reorder the terms: 0.03305785123 + 0.3636363636x + x2 = 1.909090909 + 0.03305785123 Combine like terms: 1.909090909 + 0.03305785123 = 1.94214876023 0.03305785123 + 0.3636363636x + x2 = 1.94214876023 Factor a perfect square on the left side: (x + 0.1818181818)(x + 0.1818181818) = 1.94214876023 Calculate the square root of the right side: 1.393609974 Break this problem into two subproblems by setting (x + 0.1818181818) equal to 1.393609974 and -1.393609974.Subproblem 1
x + 0.1818181818 = 1.393609974 Simplifying x + 0.1818181818 = 1.393609974 Reorder the terms: 0.1818181818 + x = 1.393609974 Solving 0.1818181818 + x = 1.393609974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = 1.393609974 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = 1.393609974 + -0.1818181818 x = 1.393609974 + -0.1818181818 Combine like terms: 1.393609974 + -0.1818181818 = 1.2117917922 x = 1.2117917922 Simplifying x = 1.2117917922Subproblem 2
x + 0.1818181818 = -1.393609974 Simplifying x + 0.1818181818 = -1.393609974 Reorder the terms: 0.1818181818 + x = -1.393609974 Solving 0.1818181818 + x = -1.393609974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = -1.393609974 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = -1.393609974 + -0.1818181818 x = -1.393609974 + -0.1818181818 Combine like terms: -1.393609974 + -0.1818181818 = -1.5754281558 x = -1.5754281558 Simplifying x = -1.5754281558Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2117917922, -1.5754281558}
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