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Simplifying (4x + 7)(6x + -9) = 118 Reorder the terms: (7 + 4x)(6x + -9) = 118 Reorder the terms: (7 + 4x)(-9 + 6x) = 118 Multiply (7 + 4x) * (-9 + 6x) (7(-9 + 6x) + 4x * (-9 + 6x)) = 118 ((-9 * 7 + 6x * 7) + 4x * (-9 + 6x)) = 118 ((-63 + 42x) + 4x * (-9 + 6x)) = 118 (-63 + 42x + (-9 * 4x + 6x * 4x)) = 118 (-63 + 42x + (-36x + 24x2)) = 118 Combine like terms: 42x + -36x = 6x (-63 + 6x + 24x2) = 118 Solving -63 + 6x + 24x2 = 118 Solving for variable 'x'. Reorder the terms: -63 + -118 + 6x + 24x2 = 118 + -118 Combine like terms: -63 + -118 = -181 -181 + 6x + 24x2 = 118 + -118 Combine like terms: 118 + -118 = 0 -181 + 6x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -7.541666667 + 0.25x + x2 = 0 Move the constant term to the right: Add '7.541666667' to each side of the equation. -7.541666667 + 0.25x + 7.541666667 + x2 = 0 + 7.541666667 Reorder the terms: -7.541666667 + 7.541666667 + 0.25x + x2 = 0 + 7.541666667 Combine like terms: -7.541666667 + 7.541666667 = 0.000000000 0.000000000 + 0.25x + x2 = 0 + 7.541666667 0.25x + x2 = 0 + 7.541666667 Combine like terms: 0 + 7.541666667 = 7.541666667 0.25x + x2 = 7.541666667 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 7.541666667 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 7.541666667 + 0.015625 Combine like terms: 7.541666667 + 0.015625 = 7.557291667 0.015625 + 0.25x + x2 = 7.557291667 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 7.557291667 Calculate the square root of the right side: 2.749052867 Break this problem into two subproblems by setting (x + 0.125) equal to 2.749052867 and -2.749052867.Subproblem 1
x + 0.125 = 2.749052867 Simplifying x + 0.125 = 2.749052867 Reorder the terms: 0.125 + x = 2.749052867 Solving 0.125 + x = 2.749052867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 2.749052867 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 2.749052867 + -0.125 x = 2.749052867 + -0.125 Combine like terms: 2.749052867 + -0.125 = 2.624052867 x = 2.624052867 Simplifying x = 2.624052867Subproblem 2
x + 0.125 = -2.749052867 Simplifying x + 0.125 = -2.749052867 Reorder the terms: 0.125 + x = -2.749052867 Solving 0.125 + x = -2.749052867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -2.749052867 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -2.749052867 + -0.125 x = -2.749052867 + -0.125 Combine like terms: -2.749052867 + -0.125 = -2.874052867 x = -2.874052867 Simplifying x = -2.874052867Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.624052867, -2.874052867}
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