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Simplifying (3x + 6)(x + -4) = 8 Reorder the terms: (6 + 3x)(x + -4) = 8 Reorder the terms: (6 + 3x)(-4 + x) = 8 Multiply (6 + 3x) * (-4 + x) (6(-4 + x) + 3x * (-4 + x)) = 8 ((-4 * 6 + x * 6) + 3x * (-4 + x)) = 8 ((-24 + 6x) + 3x * (-4 + x)) = 8 (-24 + 6x + (-4 * 3x + x * 3x)) = 8 (-24 + 6x + (-12x + 3x2)) = 8 Combine like terms: 6x + -12x = -6x (-24 + -6x + 3x2) = 8 Solving -24 + -6x + 3x2 = 8 Solving for variable 'x'. Reorder the terms: -24 + -8 + -6x + 3x2 = 8 + -8 Combine like terms: -24 + -8 = -32 -32 + -6x + 3x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -32 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.66666667 + -2x + x2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + -2x + 10.66666667 + x2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + -2x + x2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + -2x + x2 = 0 + 10.66666667 -2x + x2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 -2x + x2 = 10.66666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 10.66666667 + 1 Reorder the terms: 1 + -2x + x2 = 10.66666667 + 1 Combine like terms: 10.66666667 + 1 = 11.66666667 1 + -2x + x2 = 11.66666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 11.66666667 Calculate the square root of the right side: 3.415650256 Break this problem into two subproblems by setting (x + -1) equal to 3.415650256 and -3.415650256.Subproblem 1
x + -1 = 3.415650256 Simplifying x + -1 = 3.415650256 Reorder the terms: -1 + x = 3.415650256 Solving -1 + x = 3.415650256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.415650256 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.415650256 + 1 x = 3.415650256 + 1 Combine like terms: 3.415650256 + 1 = 4.415650256 x = 4.415650256 Simplifying x = 4.415650256Subproblem 2
x + -1 = -3.415650256 Simplifying x + -1 = -3.415650256 Reorder the terms: -1 + x = -3.415650256 Solving -1 + x = -3.415650256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.415650256 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.415650256 + 1 x = -3.415650256 + 1 Combine like terms: -3.415650256 + 1 = -2.415650256 x = -2.415650256 Simplifying x = -2.415650256Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.415650256, -2.415650256}
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