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Simplifying 6x * 6x + -5x = 56 Reorder the terms for easier multiplication: 6 * 6x * x + -5x = 56 Multiply 6 * 6 36x * x + -5x = 56 Multiply x * x 36x2 + -5x = 56 Reorder the terms: -5x + 36x2 = 56 Solving -5x + 36x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + -5x + 36x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + -5x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -1.555555556 + -0.1388888889x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + -0.1388888889x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + -0.1388888889x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + -0.1388888889x + x2 = 0 + 1.555555556 -0.1388888889x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 -0.1388888889x + x2 = 1.555555556 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 = 1.555555556 + 0.004822530865 Reorder the terms: 0.004822530865 + -0.1388888889x + x2 = 1.555555556 + 0.004822530865 Combine like terms: 1.555555556 + 0.004822530865 = 1.560378086865 0.004822530865 + -0.1388888889x + x2 = 1.560378086865 Factor a perfect square on the left side: (x + -0.06944444445)(x + -0.06944444445) = 1.560378086865 Calculate the square root of the right side: 1.249150946 Break this problem into two subproblems by setting (x + -0.06944444445) equal to 1.249150946 and -1.249150946.Subproblem 1
x + -0.06944444445 = 1.249150946 Simplifying x + -0.06944444445 = 1.249150946 Reorder the terms: -0.06944444445 + x = 1.249150946 Solving -0.06944444445 + x = 1.249150946 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 = 1.249150946 + 0.06944444445 Combine like terms: -0.06944444445 + 0.06944444445 = 0.00000000000 0.00000000000 + x = 1.249150946 + 0.06944444445 x = 1.249150946 + 0.06944444445 Combine like terms: 1.249150946 + 0.06944444445 = 1.31859539045 x = 1.31859539045 Simplifying x = 1.31859539045Subproblem 2
x + -0.06944444445 = -1.249150946 Simplifying x + -0.06944444445 = -1.249150946 Reorder the terms: -0.06944444445 + x = -1.249150946 Solving -0.06944444445 + x = -1.249150946 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 = -1.249150946 + 0.06944444445 Combine like terms: -0.06944444445 + 0.06944444445 = 0.00000000000 0.00000000000 + x = -1.249150946 + 0.06944444445 x = -1.249150946 + 0.06944444445 Combine like terms: -1.249150946 + 0.06944444445 = -1.17970650155 x = -1.17970650155 Simplifying x = -1.17970650155Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.31859539045, -1.17970650155}
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