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Simplifying 6(6x2 + -1) = 5x Reorder the terms: 6(-1 + 6x2) = 5x (-1 * 6 + 6x2 * 6) = 5x (-6 + 36x2) = 5x Solving -6 + 36x2 = 5x Solving for variable 'x'. Reorder the terms: -6 + -5x + 36x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -6 + -5x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.1666666667 + -0.1388888889x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -0.1388888889x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -0.1388888889x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -0.1388888889x + x2 = 0 + 0.1666666667 -0.1388888889x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -0.1388888889x + x2 = 0.1666666667 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 = 0.1666666667 + 0.004822530865 Reorder the terms: 0.004822530865 + -0.1388888889x + x2 = 0.1666666667 + 0.004822530865 Combine like terms: 0.1666666667 + 0.004822530865 = 0.171489197565 0.004822530865 + -0.1388888889x + x2 = 0.171489197565 Factor a perfect square on the left side: (x + -0.06944444445)(x + -0.06944444445) = 0.171489197565 Calculate the square root of the right side: 0.414112542 Break this problem into two subproblems by setting (x + -0.06944444445) equal to 0.414112542 and -0.414112542.Subproblem 1
x + -0.06944444445 = 0.414112542 Simplifying x + -0.06944444445 = 0.414112542 Reorder the terms: -0.06944444445 + x = 0.414112542 Solving -0.06944444445 + x = 0.414112542 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 = 0.414112542 + 0.06944444445 Combine like terms: -0.06944444445 + 0.06944444445 = 0.00000000000 0.00000000000 + x = 0.414112542 + 0.06944444445 x = 0.414112542 + 0.06944444445 Combine like terms: 0.414112542 + 0.06944444445 = 0.48355698645 x = 0.48355698645 Simplifying x = 0.48355698645Subproblem 2
x + -0.06944444445 = -0.414112542 Simplifying x + -0.06944444445 = -0.414112542 Reorder the terms: -0.06944444445 + x = -0.414112542 Solving -0.06944444445 + x = -0.414112542 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 = -0.414112542 + 0.06944444445 Combine like terms: -0.06944444445 + 0.06944444445 = 0.00000000000 0.00000000000 + x = -0.414112542 + 0.06944444445 x = -0.414112542 + 0.06944444445 Combine like terms: -0.414112542 + 0.06944444445 = -0.34466809755 x = -0.34466809755 Simplifying x = -0.34466809755Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.48355698645, -0.34466809755}
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