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Simplifying (4x + -5)(3x + 20) = 180 Reorder the terms: (-5 + 4x)(3x + 20) = 180 Reorder the terms: (-5 + 4x)(20 + 3x) = 180 Multiply (-5 + 4x) * (20 + 3x) (-5(20 + 3x) + 4x * (20 + 3x)) = 180 ((20 * -5 + 3x * -5) + 4x * (20 + 3x)) = 180 ((-100 + -15x) + 4x * (20 + 3x)) = 180 (-100 + -15x + (20 * 4x + 3x * 4x)) = 180 (-100 + -15x + (80x + 12x2)) = 180 Combine like terms: -15x + 80x = 65x (-100 + 65x + 12x2) = 180 Solving -100 + 65x + 12x2 = 180 Solving for variable 'x'. Reorder the terms: -100 + -180 + 65x + 12x2 = 180 + -180 Combine like terms: -100 + -180 = -280 -280 + 65x + 12x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -280 + 65x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -23.33333333 + 5.416666667x + x2 = 0 Move the constant term to the right: Add '23.33333333' to each side of the equation. -23.33333333 + 5.416666667x + 23.33333333 + x2 = 0 + 23.33333333 Reorder the terms: -23.33333333 + 23.33333333 + 5.416666667x + x2 = 0 + 23.33333333 Combine like terms: -23.33333333 + 23.33333333 = 0.00000000 0.00000000 + 5.416666667x + x2 = 0 + 23.33333333 5.416666667x + x2 = 0 + 23.33333333 Combine like terms: 0 + 23.33333333 = 23.33333333 5.416666667x + x2 = 23.33333333 The x term is 5.416666667x. Take half its coefficient (2.708333334). Square it (7.335069448) and add it to both sides. Add '7.335069448' to each side of the equation. 5.416666667x + 7.335069448 + x2 = 23.33333333 + 7.335069448 Reorder the terms: 7.335069448 + 5.416666667x + x2 = 23.33333333 + 7.335069448 Combine like terms: 23.33333333 + 7.335069448 = 30.668402778 7.335069448 + 5.416666667x + x2 = 30.668402778 Factor a perfect square on the left side: (x + 2.708333334)(x + 2.708333334) = 30.668402778 Calculate the square root of the right side: 5.537905992 Break this problem into two subproblems by setting (x + 2.708333334) equal to 5.537905992 and -5.537905992.Subproblem 1
x + 2.708333334 = 5.537905992 Simplifying x + 2.708333334 = 5.537905992 Reorder the terms: 2.708333334 + x = 5.537905992 Solving 2.708333334 + x = 5.537905992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.708333334' to each side of the equation. 2.708333334 + -2.708333334 + x = 5.537905992 + -2.708333334 Combine like terms: 2.708333334 + -2.708333334 = 0.000000000 0.000000000 + x = 5.537905992 + -2.708333334 x = 5.537905992 + -2.708333334 Combine like terms: 5.537905992 + -2.708333334 = 2.829572658 x = 2.829572658 Simplifying x = 2.829572658Subproblem 2
x + 2.708333334 = -5.537905992 Simplifying x + 2.708333334 = -5.537905992 Reorder the terms: 2.708333334 + x = -5.537905992 Solving 2.708333334 + x = -5.537905992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.708333334' to each side of the equation. 2.708333334 + -2.708333334 + x = -5.537905992 + -2.708333334 Combine like terms: 2.708333334 + -2.708333334 = 0.000000000 0.000000000 + x = -5.537905992 + -2.708333334 x = -5.537905992 + -2.708333334 Combine like terms: -5.537905992 + -2.708333334 = -8.246239326 x = -8.246239326 Simplifying x = -8.246239326Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.829572658, -8.246239326}
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