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Simplifying (6 + -1x)(x + -4) = (6 + -1x)(-2 + 0.5x) Reorder the terms: (6 + -1x)(-4 + x) = (6 + -1x)(-2 + 0.5x) Multiply (6 + -1x) * (-4 + x) (6(-4 + x) + -1x * (-4 + x)) = (6 + -1x)(-2 + 0.5x) ((-4 * 6 + x * 6) + -1x * (-4 + x)) = (6 + -1x)(-2 + 0.5x) ((-24 + 6x) + -1x * (-4 + x)) = (6 + -1x)(-2 + 0.5x) (-24 + 6x + (-4 * -1x + x * -1x)) = (6 + -1x)(-2 + 0.5x) (-24 + 6x + (4x + -1x2)) = (6 + -1x)(-2 + 0.5x) Combine like terms: 6x + 4x = 10x (-24 + 10x + -1x2) = (6 + -1x)(-2 + 0.5x) Multiply (6 + -1x) * (-2 + 0.5x) -24 + 10x + -1x2 = (6(-2 + 0.5x) + -1x * (-2 + 0.5x)) -24 + 10x + -1x2 = ((-2 * 6 + 0.5x * 6) + -1x * (-2 + 0.5x)) -24 + 10x + -1x2 = ((-12 + 3x) + -1x * (-2 + 0.5x)) -24 + 10x + -1x2 = (-12 + 3x + (-2 * -1x + 0.5x * -1x)) -24 + 10x + -1x2 = (-12 + 3x + (2x + -0.5x2)) Combine like terms: 3x + 2x = 5x -24 + 10x + -1x2 = (-12 + 5x + -0.5x2) Solving -24 + 10x + -1x2 = -12 + 5x + -0.5x2 Solving for variable 'x'. Reorder the terms: -24 + 12 + 10x + -5x + -1x2 + 0.5x2 = -12 + 5x + -0.5x2 + 12 + -5x + 0.5x2 Combine like terms: -24 + 12 = -12 -12 + 10x + -5x + -1x2 + 0.5x2 = -12 + 5x + -0.5x2 + 12 + -5x + 0.5x2 Combine like terms: 10x + -5x = 5x -12 + 5x + -1x2 + 0.5x2 = -12 + 5x + -0.5x2 + 12 + -5x + 0.5x2 Combine like terms: -1x2 + 0.5x2 = -0.5x2 -12 + 5x + -0.5x2 = -12 + 5x + -0.5x2 + 12 + -5x + 0.5x2 Reorder the terms: -12 + 5x + -0.5x2 = -12 + 12 + 5x + -5x + -0.5x2 + 0.5x2 Combine like terms: -12 + 12 = 0 -12 + 5x + -0.5x2 = 0 + 5x + -5x + -0.5x2 + 0.5x2 -12 + 5x + -0.5x2 = 5x + -5x + -0.5x2 + 0.5x2 Combine like terms: 5x + -5x = 0 -12 + 5x + -0.5x2 = 0 + -0.5x2 + 0.5x2 -12 + 5x + -0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -12 + 5x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 24 + -10x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -10x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -10x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -10x + x2 = 0 + -24 -10x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -10x + x2 = -24 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -24 + 25 Reorder the terms: 25 + -10x + x2 = -24 + 25 Combine like terms: -24 + 25 = 1 25 + -10x + x2 = 1 Factor a perfect square on the left side: (x + -5)(x + -5) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + -5) equal to 1 and -1.Subproblem 1
x + -5 = 1 Simplifying x + -5 = 1 Reorder the terms: -5 + x = 1 Solving -5 + x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 1 + 5 Combine like terms: -5 + 5 = 0 0 + x = 1 + 5 x = 1 + 5 Combine like terms: 1 + 5 = 6 x = 6 Simplifying x = 6Subproblem 2
x + -5 = -1 Simplifying x + -5 = -1 Reorder the terms: -5 + x = -1 Solving -5 + x = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -1 + 5 Combine like terms: -5 + 5 = 0 0 + x = -1 + 5 x = -1 + 5 Combine like terms: -1 + 5 = 4 x = 4 Simplifying x = 4Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, 4}
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