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Simplifying (x + -1)(3x + -4) = 576 Reorder the terms: (-1 + x)(3x + -4) = 576 Reorder the terms: (-1 + x)(-4 + 3x) = 576 Multiply (-1 + x) * (-4 + 3x) (-1(-4 + 3x) + x(-4 + 3x)) = 576 ((-4 * -1 + 3x * -1) + x(-4 + 3x)) = 576 ((4 + -3x) + x(-4 + 3x)) = 576 (4 + -3x + (-4 * x + 3x * x)) = 576 (4 + -3x + (-4x + 3x2)) = 576 Combine like terms: -3x + -4x = -7x (4 + -7x + 3x2) = 576 Solving 4 + -7x + 3x2 = 576 Solving for variable 'x'. Reorder the terms: 4 + -576 + -7x + 3x2 = 576 + -576 Combine like terms: 4 + -576 = -572 -572 + -7x + 3x2 = 576 + -576 Combine like terms: 576 + -576 = 0 -572 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -190.6666667 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '190.6666667' to each side of the equation. -190.6666667 + -2.333333333x + 190.6666667 + x2 = 0 + 190.6666667 Reorder the terms: -190.6666667 + 190.6666667 + -2.333333333x + x2 = 0 + 190.6666667 Combine like terms: -190.6666667 + 190.6666667 = 0.0000000 0.0000000 + -2.333333333x + x2 = 0 + 190.6666667 -2.333333333x + x2 = 0 + 190.6666667 Combine like terms: 0 + 190.6666667 = 190.6666667 -2.333333333x + x2 = 190.6666667 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 190.6666667 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 190.6666667 + 1.361111112 Combine like terms: 190.6666667 + 1.361111112 = 192.027777812 1.361111112 + -2.333333333x + x2 = 192.027777812 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 192.027777812 Calculate the square root of the right side: 13.85740877 Break this problem into two subproblems by setting (x + -1.166666667) equal to 13.85740877 and -13.85740877.Subproblem 1
x + -1.166666667 = 13.85740877 Simplifying x + -1.166666667 = 13.85740877 Reorder the terms: -1.166666667 + x = 13.85740877 Solving -1.166666667 + x = 13.85740877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 13.85740877 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 13.85740877 + 1.166666667 x = 13.85740877 + 1.166666667 Combine like terms: 13.85740877 + 1.166666667 = 15.024075437 x = 15.024075437 Simplifying x = 15.024075437Subproblem 2
x + -1.166666667 = -13.85740877 Simplifying x + -1.166666667 = -13.85740877 Reorder the terms: -1.166666667 + x = -13.85740877 Solving -1.166666667 + x = -13.85740877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -13.85740877 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -13.85740877 + 1.166666667 x = -13.85740877 + 1.166666667 Combine like terms: -13.85740877 + 1.166666667 = -12.690742103 x = -12.690742103 Simplifying x = -12.690742103Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.024075437, -12.690742103}
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