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Simplifying (4x + 2)(3x + -9) = x Reorder the terms: (2 + 4x)(3x + -9) = x Reorder the terms: (2 + 4x)(-9 + 3x) = x Multiply (2 + 4x) * (-9 + 3x) (2(-9 + 3x) + 4x * (-9 + 3x)) = x ((-9 * 2 + 3x * 2) + 4x * (-9 + 3x)) = x ((-18 + 6x) + 4x * (-9 + 3x)) = x (-18 + 6x + (-9 * 4x + 3x * 4x)) = x (-18 + 6x + (-36x + 12x2)) = x Combine like terms: 6x + -36x = -30x (-18 + -30x + 12x2) = x Solving -18 + -30x + 12x2 = x Solving for variable 'x'. Reorder the terms: -18 + -30x + -1x + 12x2 = x + -1x Combine like terms: -30x + -1x = -31x -18 + -31x + 12x2 = x + -1x Combine like terms: x + -1x = 0 -18 + -31x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.5 + -2.583333333x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.583333333x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.583333333x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.583333333x + x2 = 0 + 1.5 -2.583333333x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.583333333x + x2 = 1.5 The x term is -2.583333333x. Take half its coefficient (-1.291666667). Square it (1.668402779) and add it to both sides. Add '1.668402779' to each side of the equation. -2.583333333x + 1.668402779 + x2 = 1.5 + 1.668402779 Reorder the terms: 1.668402779 + -2.583333333x + x2 = 1.5 + 1.668402779 Combine like terms: 1.5 + 1.668402779 = 3.168402779 1.668402779 + -2.583333333x + x2 = 3.168402779 Factor a perfect square on the left side: (x + -1.291666667)(x + -1.291666667) = 3.168402779 Calculate the square root of the right side: 1.780000781 Break this problem into two subproblems by setting (x + -1.291666667) equal to 1.780000781 and -1.780000781.Subproblem 1
x + -1.291666667 = 1.780000781 Simplifying x + -1.291666667 = 1.780000781 Reorder the terms: -1.291666667 + x = 1.780000781 Solving -1.291666667 + x = 1.780000781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.291666667' to each side of the equation. -1.291666667 + 1.291666667 + x = 1.780000781 + 1.291666667 Combine like terms: -1.291666667 + 1.291666667 = 0.000000000 0.000000000 + x = 1.780000781 + 1.291666667 x = 1.780000781 + 1.291666667 Combine like terms: 1.780000781 + 1.291666667 = 3.071667448 x = 3.071667448 Simplifying x = 3.071667448Subproblem 2
x + -1.291666667 = -1.780000781 Simplifying x + -1.291666667 = -1.780000781 Reorder the terms: -1.291666667 + x = -1.780000781 Solving -1.291666667 + x = -1.780000781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.291666667' to each side of the equation. -1.291666667 + 1.291666667 + x = -1.780000781 + 1.291666667 Combine like terms: -1.291666667 + 1.291666667 = 0.000000000 0.000000000 + x = -1.780000781 + 1.291666667 x = -1.780000781 + 1.291666667 Combine like terms: -1.780000781 + 1.291666667 = -0.488334114 x = -0.488334114 Simplifying x = -0.488334114Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.071667448, -0.488334114}
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