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Simplifying (2x + 1)(x + 4) = 6 Reorder the terms: (1 + 2x)(x + 4) = 6 Reorder the terms: (1 + 2x)(4 + x) = 6 Multiply (1 + 2x) * (4 + x) (1(4 + x) + 2x * (4 + x)) = 6 ((4 * 1 + x * 1) + 2x * (4 + x)) = 6 ((4 + 1x) + 2x * (4 + x)) = 6 (4 + 1x + (4 * 2x + x * 2x)) = 6 (4 + 1x + (8x + 2x2)) = 6 Combine like terms: 1x + 8x = 9x (4 + 9x + 2x2) = 6 Solving 4 + 9x + 2x2 = 6 Solving for variable 'x'. Reorder the terms: 4 + -6 + 9x + 2x2 = 6 + -6 Combine like terms: 4 + -6 = -2 -2 + 9x + 2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -2 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + 4.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 4.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 4.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4.5x + x2 = 0 + 1 4.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 4.5x + x2 = 1 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 1 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 1 + 5.0625 Combine like terms: 1 + 5.0625 = 6.0625 5.0625 + 4.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + 2.25) equal to 2.46221445 and -2.46221445.Subproblem 1
x + 2.25 = 2.46221445 Simplifying x + 2.25 = 2.46221445 Reorder the terms: 2.25 + x = 2.46221445 Solving 2.25 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.46221445 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.46221445 + -2.25 x = 2.46221445 + -2.25 Combine like terms: 2.46221445 + -2.25 = 0.21221445 x = 0.21221445 Simplifying x = 0.21221445Subproblem 2
x + 2.25 = -2.46221445 Simplifying x + 2.25 = -2.46221445 Reorder the terms: 2.25 + x = -2.46221445 Solving 2.25 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.46221445 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.46221445 + -2.25 x = -2.46221445 + -2.25 Combine like terms: -2.46221445 + -2.25 = -4.71221445 x = -4.71221445 Simplifying x = -4.71221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.21221445, -4.71221445}
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