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Simplifying 3x(x + -1) = 2(x + 27) Reorder the terms: 3x(-1 + x) = 2(x + 27) (-1 * 3x + x * 3x) = 2(x + 27) (-3x + 3x2) = 2(x + 27) Reorder the terms: -3x + 3x2 = 2(27 + x) -3x + 3x2 = (27 * 2 + x * 2) -3x + 3x2 = (54 + 2x) Solving -3x + 3x2 = 54 + 2x Solving for variable 'x'. Reorder the terms: -54 + -3x + -2x + 3x2 = 54 + 2x + -54 + -2x Combine like terms: -3x + -2x = -5x -54 + -5x + 3x2 = 54 + 2x + -54 + -2x Reorder the terms: -54 + -5x + 3x2 = 54 + -54 + 2x + -2x Combine like terms: 54 + -54 = 0 -54 + -5x + 3x2 = 0 + 2x + -2x -54 + -5x + 3x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -54 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -18 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -1.666666667x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -1.666666667x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1.666666667x + x2 = 0 + 18 -1.666666667x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -1.666666667x + x2 = 18 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 18 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 18 + 0.6944444447 Combine like terms: 18 + 0.6944444447 = 18.6944444447 0.6944444447 + -1.666666667x + x2 = 18.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 18.6944444447 Calculate the square root of the right side: 4.323707257 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 4.323707257 and -4.323707257.Subproblem 1
x + -0.8333333335 = 4.323707257 Simplifying x + -0.8333333335 = 4.323707257 Reorder the terms: -0.8333333335 + x = 4.323707257 Solving -0.8333333335 + x = 4.323707257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 4.323707257 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 4.323707257 + 0.8333333335 x = 4.323707257 + 0.8333333335 Combine like terms: 4.323707257 + 0.8333333335 = 5.1570405905 x = 5.1570405905 Simplifying x = 5.1570405905Subproblem 2
x + -0.8333333335 = -4.323707257 Simplifying x + -0.8333333335 = -4.323707257 Reorder the terms: -0.8333333335 + x = -4.323707257 Solving -0.8333333335 + x = -4.323707257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -4.323707257 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -4.323707257 + 0.8333333335 x = -4.323707257 + 0.8333333335 Combine like terms: -4.323707257 + 0.8333333335 = -3.4903739235 x = -3.4903739235 Simplifying x = -3.4903739235Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.1570405905, -3.4903739235}
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