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Simplifying (6x + -4)(6x + -4) = 41 Reorder the terms: (-4 + 6x)(6x + -4) = 41 Reorder the terms: (-4 + 6x)(-4 + 6x) = 41 Multiply (-4 + 6x) * (-4 + 6x) (-4(-4 + 6x) + 6x * (-4 + 6x)) = 41 ((-4 * -4 + 6x * -4) + 6x * (-4 + 6x)) = 41 ((16 + -24x) + 6x * (-4 + 6x)) = 41 (16 + -24x + (-4 * 6x + 6x * 6x)) = 41 (16 + -24x + (-24x + 36x2)) = 41 Combine like terms: -24x + -24x = -48x (16 + -48x + 36x2) = 41 Solving 16 + -48x + 36x2 = 41 Solving for variable 'x'. Reorder the terms: 16 + -41 + -48x + 36x2 = 41 + -41 Combine like terms: 16 + -41 = -25 -25 + -48x + 36x2 = 41 + -41 Combine like terms: 41 + -41 = 0 -25 + -48x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.6944444444 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '0.6944444444' to each side of the equation. -0.6944444444 + -1.333333333x + 0.6944444444 + x2 = 0 + 0.6944444444 Reorder the terms: -0.6944444444 + 0.6944444444 + -1.333333333x + x2 = 0 + 0.6944444444 Combine like terms: -0.6944444444 + 0.6944444444 = 0.0000000000 0.0000000000 + -1.333333333x + x2 = 0 + 0.6944444444 -1.333333333x + x2 = 0 + 0.6944444444 Combine like terms: 0 + 0.6944444444 = 0.6944444444 -1.333333333x + x2 = 0.6944444444 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 0.6944444444 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 0.6944444444 + 0.4444444442 Combine like terms: 0.6944444444 + 0.4444444442 = 1.1388888886 0.4444444442 + -1.333333333x + x2 = 1.1388888886 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 1.1388888886 Calculate the square root of the right side: 1.067187373 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 1.067187373 and -1.067187373.Subproblem 1
x + -0.6666666665 = 1.067187373 Simplifying x + -0.6666666665 = 1.067187373 Reorder the terms: -0.6666666665 + x = 1.067187373 Solving -0.6666666665 + x = 1.067187373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.067187373 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.067187373 + 0.6666666665 x = 1.067187373 + 0.6666666665 Combine like terms: 1.067187373 + 0.6666666665 = 1.7338540395 x = 1.7338540395 Simplifying x = 1.7338540395Subproblem 2
x + -0.6666666665 = -1.067187373 Simplifying x + -0.6666666665 = -1.067187373 Reorder the terms: -0.6666666665 + x = -1.067187373 Solving -0.6666666665 + x = -1.067187373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.067187373 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.067187373 + 0.6666666665 x = -1.067187373 + 0.6666666665 Combine like terms: -1.067187373 + 0.6666666665 = -0.4005207065 x = -0.4005207065 Simplifying x = -0.4005207065Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7338540395, -0.4005207065}
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