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Simplifying (x + 6)(4x + -3) = (2x + 3) * 2 Reorder the terms: (6 + x)(4x + -3) = (2x + 3) * 2 Reorder the terms: (6 + x)(-3 + 4x) = (2x + 3) * 2 Multiply (6 + x) * (-3 + 4x) (6(-3 + 4x) + x(-3 + 4x)) = (2x + 3) * 2 ((-3 * 6 + 4x * 6) + x(-3 + 4x)) = (2x + 3) * 2 ((-18 + 24x) + x(-3 + 4x)) = (2x + 3) * 2 (-18 + 24x + (-3 * x + 4x * x)) = (2x + 3) * 2 (-18 + 24x + (-3x + 4x2)) = (2x + 3) * 2 Combine like terms: 24x + -3x = 21x (-18 + 21x + 4x2) = (2x + 3) * 2 Reorder the terms: -18 + 21x + 4x2 = (3 + 2x) * 2 Reorder the terms for easier multiplication: -18 + 21x + 4x2 = 2(3 + 2x) -18 + 21x + 4x2 = (3 * 2 + 2x * 2) -18 + 21x + 4x2 = (6 + 4x) Solving -18 + 21x + 4x2 = 6 + 4x Solving for variable 'x'. Reorder the terms: -18 + -6 + 21x + -4x + 4x2 = 6 + 4x + -6 + -4x Combine like terms: -18 + -6 = -24 -24 + 21x + -4x + 4x2 = 6 + 4x + -6 + -4x Combine like terms: 21x + -4x = 17x -24 + 17x + 4x2 = 6 + 4x + -6 + -4x Reorder the terms: -24 + 17x + 4x2 = 6 + -6 + 4x + -4x Combine like terms: 6 + -6 = 0 -24 + 17x + 4x2 = 0 + 4x + -4x -24 + 17x + 4x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -24 + 17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6 + 4.25x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 4.25x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 4.25x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4.25x + x2 = 0 + 6 4.25x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 4.25x + x2 = 6 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 6 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 6 + 4.515625 Combine like terms: 6 + 4.515625 = 10.515625 4.515625 + 4.25x + x2 = 10.515625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 10.515625 Calculate the square root of the right side: 3.242780443 Break this problem into two subproblems by setting (x + 2.125) equal to 3.242780443 and -3.242780443.Subproblem 1
x + 2.125 = 3.242780443 Simplifying x + 2.125 = 3.242780443 Reorder the terms: 2.125 + x = 3.242780443 Solving 2.125 + x = 3.242780443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 3.242780443 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 3.242780443 + -2.125 x = 3.242780443 + -2.125 Combine like terms: 3.242780443 + -2.125 = 1.117780443 x = 1.117780443 Simplifying x = 1.117780443Subproblem 2
x + 2.125 = -3.242780443 Simplifying x + 2.125 = -3.242780443 Reorder the terms: 2.125 + x = -3.242780443 Solving 2.125 + x = -3.242780443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -3.242780443 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -3.242780443 + -2.125 x = -3.242780443 + -2.125 Combine like terms: -3.242780443 + -2.125 = -5.367780443 x = -5.367780443 Simplifying x = -5.367780443Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.117780443, -5.367780443}
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