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Simplifying 6x * 6x + 5x + -4 = 0 Reorder the terms for easier multiplication: 6 * 6x * x + 5x + -4 = 0 Multiply 6 * 6 36x * x + 5x + -4 = 0 Multiply x * x 36x2 + 5x + -4 = 0 Reorder the terms: -4 + 5x + 36x2 = 0 Solving -4 + 5x + 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'. -0.1111111111 + 0.1388888889x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1388888889x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 0.1388888889x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 0.1388888889x + x2 = 0 + 0.1111111111 0.1388888889x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 0.1388888889x + x2 = 0.1111111111 The x term is 0.1388888889x. Take half its coefficient (0.06944444445). Square it (0.004822530865) and add it to both sides. Add '0.004822530865' to each side of the equation. 0.1388888889x + 0.004822530865 + x2 = 0.1111111111 + 0.004822530865 Reorder the terms: 0.004822530865 + 0.1388888889x + x2 = 0.1111111111 + 0.004822530865 Combine like terms: 0.1111111111 + 0.004822530865 = 0.115933641965 0.004822530865 + 0.1388888889x + x2 = 0.115933641965 Factor a perfect square on the left side: (x + 0.06944444445)(x + 0.06944444445) = 0.115933641965 Calculate the square root of the right side: 0.340490296 Break this problem into two subproblems by setting (x + 0.06944444445) equal to 0.340490296 and -0.340490296.Subproblem 1
x + 0.06944444445 = 0.340490296 Simplifying x + 0.06944444445 = 0.340490296 Reorder the terms: 0.06944444445 + x = 0.340490296 Solving 0.06944444445 + x = 0.340490296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06944444445' to each side of the equation. 0.06944444445 + -0.06944444445 + x = 0.340490296 + -0.06944444445 Combine like terms: 0.06944444445 + -0.06944444445 = 0.00000000000 0.00000000000 + x = 0.340490296 + -0.06944444445 x = 0.340490296 + -0.06944444445 Combine like terms: 0.340490296 + -0.06944444445 = 0.27104585155 x = 0.27104585155 Simplifying x = 0.27104585155Subproblem 2
x + 0.06944444445 = -0.340490296 Simplifying x + 0.06944444445 = -0.340490296 Reorder the terms: 0.06944444445 + x = -0.340490296 Solving 0.06944444445 + x = -0.340490296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06944444445' to each side of the equation. 0.06944444445 + -0.06944444445 + x = -0.340490296 + -0.06944444445 Combine like terms: 0.06944444445 + -0.06944444445 = 0.00000000000 0.00000000000 + x = -0.340490296 + -0.06944444445 x = -0.340490296 + -0.06944444445 Combine like terms: -0.340490296 + -0.06944444445 = -0.40993474045 x = -0.40993474045 Simplifying x = -0.40993474045Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.27104585155, -0.40993474045}
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