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Simplifying (4x + -3)(9x + -1) = 180 Reorder the terms: (-3 + 4x)(9x + -1) = 180 Reorder the terms: (-3 + 4x)(-1 + 9x) = 180 Multiply (-3 + 4x) * (-1 + 9x) (-3(-1 + 9x) + 4x * (-1 + 9x)) = 180 ((-1 * -3 + 9x * -3) + 4x * (-1 + 9x)) = 180 ((3 + -27x) + 4x * (-1 + 9x)) = 180 (3 + -27x + (-1 * 4x + 9x * 4x)) = 180 (3 + -27x + (-4x + 36x2)) = 180 Combine like terms: -27x + -4x = -31x (3 + -31x + 36x2) = 180 Solving 3 + -31x + 36x2 = 180 Solving for variable 'x'. Reorder the terms: 3 + -180 + -31x + 36x2 = 180 + -180 Combine like terms: 3 + -180 = -177 -177 + -31x + 36x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -177 + -31x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -4.916666667 + -0.8611111111x + x2 = 0 Move the constant term to the right: Add '4.916666667' to each side of the equation. -4.916666667 + -0.8611111111x + 4.916666667 + x2 = 0 + 4.916666667 Reorder the terms: -4.916666667 + 4.916666667 + -0.8611111111x + x2 = 0 + 4.916666667 Combine like terms: -4.916666667 + 4.916666667 = 0.000000000 0.000000000 + -0.8611111111x + x2 = 0 + 4.916666667 -0.8611111111x + x2 = 0 + 4.916666667 Combine like terms: 0 + 4.916666667 = 4.916666667 -0.8611111111x + x2 = 4.916666667 The x term is -0.8611111111x. Take half its coefficient (-0.4305555556). Square it (0.1853780865) and add it to both sides. Add '0.1853780865' to each side of the equation. -0.8611111111x + 0.1853780865 + x2 = 4.916666667 + 0.1853780865 Reorder the terms: 0.1853780865 + -0.8611111111x + x2 = 4.916666667 + 0.1853780865 Combine like terms: 4.916666667 + 0.1853780865 = 5.1020447535 0.1853780865 + -0.8611111111x + x2 = 5.1020447535 Factor a perfect square on the left side: (x + -0.4305555556)(x + -0.4305555556) = 5.1020447535 Calculate the square root of the right side: 2.258770629 Break this problem into two subproblems by setting (x + -0.4305555556) equal to 2.258770629 and -2.258770629.Subproblem 1
x + -0.4305555556 = 2.258770629 Simplifying x + -0.4305555556 = 2.258770629 Reorder the terms: -0.4305555556 + x = 2.258770629 Solving -0.4305555556 + x = 2.258770629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4305555556' to each side of the equation. -0.4305555556 + 0.4305555556 + x = 2.258770629 + 0.4305555556 Combine like terms: -0.4305555556 + 0.4305555556 = 0.0000000000 0.0000000000 + x = 2.258770629 + 0.4305555556 x = 2.258770629 + 0.4305555556 Combine like terms: 2.258770629 + 0.4305555556 = 2.6893261846 x = 2.6893261846 Simplifying x = 2.6893261846Subproblem 2
x + -0.4305555556 = -2.258770629 Simplifying x + -0.4305555556 = -2.258770629 Reorder the terms: -0.4305555556 + x = -2.258770629 Solving -0.4305555556 + x = -2.258770629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4305555556' to each side of the equation. -0.4305555556 + 0.4305555556 + x = -2.258770629 + 0.4305555556 Combine like terms: -0.4305555556 + 0.4305555556 = 0.0000000000 0.0000000000 + x = -2.258770629 + 0.4305555556 x = -2.258770629 + 0.4305555556 Combine like terms: -2.258770629 + 0.4305555556 = -1.8282150734 x = -1.8282150734 Simplifying x = -1.8282150734Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6893261846, -1.8282150734}
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