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Simplifying (3x + -7)(4x + 5) = 180 Reorder the terms: (-7 + 3x)(4x + 5) = 180 Reorder the terms: (-7 + 3x)(5 + 4x) = 180 Multiply (-7 + 3x) * (5 + 4x) (-7(5 + 4x) + 3x * (5 + 4x)) = 180 ((5 * -7 + 4x * -7) + 3x * (5 + 4x)) = 180 ((-35 + -28x) + 3x * (5 + 4x)) = 180 (-35 + -28x + (5 * 3x + 4x * 3x)) = 180 (-35 + -28x + (15x + 12x2)) = 180 Combine like terms: -28x + 15x = -13x (-35 + -13x + 12x2) = 180 Solving -35 + -13x + 12x2 = 180 Solving for variable 'x'. Reorder the terms: -35 + -180 + -13x + 12x2 = 180 + -180 Combine like terms: -35 + -180 = -215 -215 + -13x + 12x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -215 + -13x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -17.91666667 + -1.083333333x + x2 = 0 Move the constant term to the right: Add '17.91666667' to each side of the equation. -17.91666667 + -1.083333333x + 17.91666667 + x2 = 0 + 17.91666667 Reorder the terms: -17.91666667 + 17.91666667 + -1.083333333x + x2 = 0 + 17.91666667 Combine like terms: -17.91666667 + 17.91666667 = 0.00000000 0.00000000 + -1.083333333x + x2 = 0 + 17.91666667 -1.083333333x + x2 = 0 + 17.91666667 Combine like terms: 0 + 17.91666667 = 17.91666667 -1.083333333x + x2 = 17.91666667 The x term is -1.083333333x. Take half its coefficient (-0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. -1.083333333x + 0.2934027776 + x2 = 17.91666667 + 0.2934027776 Reorder the terms: 0.2934027776 + -1.083333333x + x2 = 17.91666667 + 0.2934027776 Combine like terms: 17.91666667 + 0.2934027776 = 18.2100694476 0.2934027776 + -1.083333333x + x2 = 18.2100694476 Factor a perfect square on the left side: (x + -0.5416666665)(x + -0.5416666665) = 18.2100694476 Calculate the square root of the right side: 4.267325796 Break this problem into two subproblems by setting (x + -0.5416666665) equal to 4.267325796 and -4.267325796.Subproblem 1
x + -0.5416666665 = 4.267325796 Simplifying x + -0.5416666665 = 4.267325796 Reorder the terms: -0.5416666665 + x = 4.267325796 Solving -0.5416666665 + x = 4.267325796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + x = 4.267325796 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + x = 4.267325796 + 0.5416666665 x = 4.267325796 + 0.5416666665 Combine like terms: 4.267325796 + 0.5416666665 = 4.8089924625 x = 4.8089924625 Simplifying x = 4.8089924625Subproblem 2
x + -0.5416666665 = -4.267325796 Simplifying x + -0.5416666665 = -4.267325796 Reorder the terms: -0.5416666665 + x = -4.267325796 Solving -0.5416666665 + x = -4.267325796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + x = -4.267325796 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + x = -4.267325796 + 0.5416666665 x = -4.267325796 + 0.5416666665 Combine like terms: -4.267325796 + 0.5416666665 = -3.7256591295 x = -3.7256591295 Simplifying x = -3.7256591295Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.8089924625, -3.7256591295}
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