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Simplifying (3x + -4)(3x + -4) = 42 Reorder the terms: (-4 + 3x)(3x + -4) = 42 Reorder the terms: (-4 + 3x)(-4 + 3x) = 42 Multiply (-4 + 3x) * (-4 + 3x) (-4(-4 + 3x) + 3x * (-4 + 3x)) = 42 ((-4 * -4 + 3x * -4) + 3x * (-4 + 3x)) = 42 ((16 + -12x) + 3x * (-4 + 3x)) = 42 (16 + -12x + (-4 * 3x + 3x * 3x)) = 42 (16 + -12x + (-12x + 9x2)) = 42 Combine like terms: -12x + -12x = -24x (16 + -24x + 9x2) = 42 Solving 16 + -24x + 9x2 = 42 Solving for variable 'x'. Reorder the terms: 16 + -42 + -24x + 9x2 = 42 + -42 Combine like terms: 16 + -42 = -26 -26 + -24x + 9x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -26 + -24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.888888889 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '2.888888889' to each side of the equation. -2.888888889 + -2.666666667x + 2.888888889 + x2 = 0 + 2.888888889 Reorder the terms: -2.888888889 + 2.888888889 + -2.666666667x + x2 = 0 + 2.888888889 Combine like terms: -2.888888889 + 2.888888889 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + 2.888888889 -2.666666667x + x2 = 0 + 2.888888889 Combine like terms: 0 + 2.888888889 = 2.888888889 -2.666666667x + x2 = 2.888888889 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 2.888888889 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 2.888888889 + 1.777777780 Combine like terms: 2.888888889 + 1.777777780 = 4.666666669 1.777777780 + -2.666666667x + x2 = 4.666666669 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 4.666666669 Calculate the square root of the right side: 2.1602469 Break this problem into two subproblems by setting (x + -1.333333334) equal to 2.1602469 and -2.1602469.Subproblem 1
x + -1.333333334 = 2.1602469 Simplifying x + -1.333333334 = 2.1602469 Reorder the terms: -1.333333334 + x = 2.1602469 Solving -1.333333334 + x = 2.1602469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 2.1602469 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 2.1602469 + 1.333333334 x = 2.1602469 + 1.333333334 Combine like terms: 2.1602469 + 1.333333334 = 3.493580234 x = 3.493580234 Simplifying x = 3.493580234Subproblem 2
x + -1.333333334 = -2.1602469 Simplifying x + -1.333333334 = -2.1602469 Reorder the terms: -1.333333334 + x = -2.1602469 Solving -1.333333334 + x = -2.1602469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -2.1602469 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -2.1602469 + 1.333333334 x = -2.1602469 + 1.333333334 Combine like terms: -2.1602469 + 1.333333334 = -0.826913566 x = -0.826913566 Simplifying x = -0.826913566Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.493580234, -0.826913566}
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