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Simplifying 4(x + -6) + 3(2x + -1) + -1x(x + -6) = 0 Reorder the terms: 4(-6 + x) + 3(2x + -1) + -1x(x + -6) = 0 (-6 * 4 + x * 4) + 3(2x + -1) + -1x(x + -6) = 0 (-24 + 4x) + 3(2x + -1) + -1x(x + -6) = 0 Reorder the terms: -24 + 4x + 3(-1 + 2x) + -1x(x + -6) = 0 -24 + 4x + (-1 * 3 + 2x * 3) + -1x(x + -6) = 0 -24 + 4x + (-3 + 6x) + -1x(x + -6) = 0 Reorder the terms: -24 + 4x + -3 + 6x + -1x(-6 + x) = 0 -24 + 4x + -3 + 6x + (-6 * -1x + x * -1x) = 0 -24 + 4x + -3 + 6x + (6x + -1x2) = 0 Reorder the terms: -24 + -3 + 4x + 6x + 6x + -1x2 = 0 Combine like terms: -24 + -3 = -27 -27 + 4x + 6x + 6x + -1x2 = 0 Combine like terms: 4x + 6x = 10x -27 + 10x + 6x + -1x2 = 0 Combine like terms: 10x + 6x = 16x -27 + 16x + -1x2 = 0 Solving -27 + 16x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 27 + -16x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -16x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -16x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -16x + x2 = 0 + -27 -16x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -16x + x2 = -27 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -27 + 64 Reorder the terms: 64 + -16x + x2 = -27 + 64 Combine like terms: -27 + 64 = 37 64 + -16x + x2 = 37 Factor a perfect square on the left side: (x + -8)(x + -8) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + -8) equal to 6.08276253 and -6.08276253.Subproblem 1
x + -8 = 6.08276253 Simplifying x + -8 = 6.08276253 Reorder the terms: -8 + x = 6.08276253 Solving -8 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 6.08276253 + 8 Combine like terms: -8 + 8 = 0 0 + x = 6.08276253 + 8 x = 6.08276253 + 8 Combine like terms: 6.08276253 + 8 = 14.08276253 x = 14.08276253 Simplifying x = 14.08276253Subproblem 2
x + -8 = -6.08276253 Simplifying x + -8 = -6.08276253 Reorder the terms: -8 + x = -6.08276253 Solving -8 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -6.08276253 + 8 Combine like terms: -8 + 8 = 0 0 + x = -6.08276253 + 8 x = -6.08276253 + 8 Combine like terms: -6.08276253 + 8 = 1.91723747 x = 1.91723747 Simplifying x = 1.91723747Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.08276253, 1.91723747}
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