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Simplifying (2x + 4)(2x + -9) = x Reorder the terms: (4 + 2x)(2x + -9) = x Reorder the terms: (4 + 2x)(-9 + 2x) = x Multiply (4 + 2x) * (-9 + 2x) (4(-9 + 2x) + 2x * (-9 + 2x)) = x ((-9 * 4 + 2x * 4) + 2x * (-9 + 2x)) = x ((-36 + 8x) + 2x * (-9 + 2x)) = x (-36 + 8x + (-9 * 2x + 2x * 2x)) = x (-36 + 8x + (-18x + 4x2)) = x Combine like terms: 8x + -18x = -10x (-36 + -10x + 4x2) = x Solving -36 + -10x + 4x2 = x Solving for variable 'x'. Reorder the terms: -36 + -10x + -1x + 4x2 = x + -1x Combine like terms: -10x + -1x = -11x -36 + -11x + 4x2 = x + -1x Combine like terms: x + -1x = 0 -36 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9 + -2.75x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -2.75x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -2.75x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2.75x + x2 = 0 + 9 -2.75x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2.75x + x2 = 9 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 9 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 9 + 1.890625 Combine like terms: 9 + 1.890625 = 10.890625 1.890625 + -2.75x + x2 = 10.890625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 10.890625 Calculate the square root of the right side: 3.300094696 Break this problem into two subproblems by setting (x + -1.375) equal to 3.300094696 and -3.300094696.Subproblem 1
x + -1.375 = 3.300094696 Simplifying x + -1.375 = 3.300094696 Reorder the terms: -1.375 + x = 3.300094696 Solving -1.375 + x = 3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 3.300094696 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 3.300094696 + 1.375 x = 3.300094696 + 1.375 Combine like terms: 3.300094696 + 1.375 = 4.675094696 x = 4.675094696 Simplifying x = 4.675094696Subproblem 2
x + -1.375 = -3.300094696 Simplifying x + -1.375 = -3.300094696 Reorder the terms: -1.375 + x = -3.300094696 Solving -1.375 + x = -3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -3.300094696 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -3.300094696 + 1.375 x = -3.300094696 + 1.375 Combine like terms: -3.300094696 + 1.375 = -1.925094696 x = -1.925094696 Simplifying x = -1.925094696Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.675094696, -1.925094696}
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