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Simplifying (6x)(6x) + 11x + -35 = 0 Remove parenthesis around (6x) 6x(6x) + 11x + -35 = 0 Remove parenthesis around (6x) 6x * 6x + 11x + -35 = 0 Reorder the terms for easier multiplication: 6 * 6x * x + 11x + -35 = 0 Multiply 6 * 6 36x * x + 11x + -35 = 0 Multiply x * x 36x2 + 11x + -35 = 0 Reorder the terms: -35 + 11x + 36x2 = 0 Solving -35 + 11x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.9722222222 + 0.3055555556x + x2 = 0 Move the constant term to the right: Add '0.9722222222' to each side of the equation. -0.9722222222 + 0.3055555556x + 0.9722222222 + x2 = 0 + 0.9722222222 Reorder the terms: -0.9722222222 + 0.9722222222 + 0.3055555556x + x2 = 0 + 0.9722222222 Combine like terms: -0.9722222222 + 0.9722222222 = 0.0000000000 0.0000000000 + 0.3055555556x + x2 = 0 + 0.9722222222 0.3055555556x + x2 = 0 + 0.9722222222 Combine like terms: 0 + 0.9722222222 = 0.9722222222 0.3055555556x + x2 = 0.9722222222 The x term is 0.3055555556x. Take half its coefficient (0.1527777778). Square it (0.02334104939) and add it to both sides. Add '0.02334104939' to each side of the equation. 0.3055555556x + 0.02334104939 + x2 = 0.9722222222 + 0.02334104939 Reorder the terms: 0.02334104939 + 0.3055555556x + x2 = 0.9722222222 + 0.02334104939 Combine like terms: 0.9722222222 + 0.02334104939 = 0.99556327159 0.02334104939 + 0.3055555556x + x2 = 0.99556327159 Factor a perfect square on the left side: (x + 0.1527777778)(x + 0.1527777778) = 0.99556327159 Calculate the square root of the right side: 0.99777917 Break this problem into two subproblems by setting (x + 0.1527777778) equal to 0.99777917 and -0.99777917.Subproblem 1
x + 0.1527777778 = 0.99777917 Simplifying x + 0.1527777778 = 0.99777917 Reorder the terms: 0.1527777778 + x = 0.99777917 Solving 0.1527777778 + x = 0.99777917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1527777778' to each side of the equation. 0.1527777778 + -0.1527777778 + x = 0.99777917 + -0.1527777778 Combine like terms: 0.1527777778 + -0.1527777778 = 0.0000000000 0.0000000000 + x = 0.99777917 + -0.1527777778 x = 0.99777917 + -0.1527777778 Combine like terms: 0.99777917 + -0.1527777778 = 0.8450013922 x = 0.8450013922 Simplifying x = 0.8450013922Subproblem 2
x + 0.1527777778 = -0.99777917 Simplifying x + 0.1527777778 = -0.99777917 Reorder the terms: 0.1527777778 + x = -0.99777917 Solving 0.1527777778 + x = -0.99777917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1527777778' to each side of the equation. 0.1527777778 + -0.1527777778 + x = -0.99777917 + -0.1527777778 Combine like terms: 0.1527777778 + -0.1527777778 = 0.0000000000 0.0000000000 + x = -0.99777917 + -0.1527777778 x = -0.99777917 + -0.1527777778 Combine like terms: -0.99777917 + -0.1527777778 = -1.1505569478 x = -1.1505569478 Simplifying x = -1.1505569478Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8450013922, -1.1505569478}
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