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Simplifying (x + 6)(4x + -3) = 1 Reorder the terms: (6 + x)(4x + -3) = 1 Reorder the terms: (6 + x)(-3 + 4x) = 1 Multiply (6 + x) * (-3 + 4x) (6(-3 + 4x) + x(-3 + 4x)) = 1 ((-3 * 6 + 4x * 6) + x(-3 + 4x)) = 1 ((-18 + 24x) + x(-3 + 4x)) = 1 (-18 + 24x + (-3 * x + 4x * x)) = 1 (-18 + 24x + (-3x + 4x2)) = 1 Combine like terms: 24x + -3x = 21x (-18 + 21x + 4x2) = 1 Solving -18 + 21x + 4x2 = 1 Solving for variable 'x'. Reorder the terms: -18 + -1 + 21x + 4x2 = 1 + -1 Combine like terms: -18 + -1 = -19 -19 + 21x + 4x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -19 + 21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.75 + 5.25x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + 5.25x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + 5.25x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + 5.25x + x2 = 0 + 4.75 5.25x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 5.25x + x2 = 4.75 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = 4.75 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = 4.75 + 6.890625 Combine like terms: 4.75 + 6.890625 = 11.640625 6.890625 + 5.25x + x2 = 11.640625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 11.640625 Calculate the square root of the right side: 3.411836016 Break this problem into two subproblems by setting (x + 2.625) equal to 3.411836016 and -3.411836016.Subproblem 1
x + 2.625 = 3.411836016 Simplifying x + 2.625 = 3.411836016 Reorder the terms: 2.625 + x = 3.411836016 Solving 2.625 + x = 3.411836016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 3.411836016 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 3.411836016 + -2.625 x = 3.411836016 + -2.625 Combine like terms: 3.411836016 + -2.625 = 0.786836016 x = 0.786836016 Simplifying x = 0.786836016Subproblem 2
x + 2.625 = -3.411836016 Simplifying x + 2.625 = -3.411836016 Reorder the terms: 2.625 + x = -3.411836016 Solving 2.625 + x = -3.411836016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -3.411836016 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -3.411836016 + -2.625 x = -3.411836016 + -2.625 Combine like terms: -3.411836016 + -2.625 = -6.036836016 x = -6.036836016 Simplifying x = -6.036836016Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.786836016, -6.036836016}
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