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Simplifying 6(2x + -1)(x + 3) = 49 Reorder the terms: 6(-1 + 2x)(x + 3) = 49 Reorder the terms: 6(-1 + 2x)(3 + x) = 49 Multiply (-1 + 2x) * (3 + x) 6(-1(3 + x) + 2x * (3 + x)) = 49 6((3 * -1 + x * -1) + 2x * (3 + x)) = 49 6((-3 + -1x) + 2x * (3 + x)) = 49 6(-3 + -1x + (3 * 2x + x * 2x)) = 49 6(-3 + -1x + (6x + 2x2)) = 49 Combine like terms: -1x + 6x = 5x 6(-3 + 5x + 2x2) = 49 (-3 * 6 + 5x * 6 + 2x2 * 6) = 49 (-18 + 30x + 12x2) = 49 Solving -18 + 30x + 12x2 = 49 Solving for variable 'x'. Reorder the terms: -18 + -49 + 30x + 12x2 = 49 + -49 Combine like terms: -18 + -49 = -67 -67 + 30x + 12x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -67 + 30x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -5.583333333 + 2.5x + x2 = 0 Move the constant term to the right: Add '5.583333333' to each side of the equation. -5.583333333 + 2.5x + 5.583333333 + x2 = 0 + 5.583333333 Reorder the terms: -5.583333333 + 5.583333333 + 2.5x + x2 = 0 + 5.583333333 Combine like terms: -5.583333333 + 5.583333333 = 0.000000000 0.000000000 + 2.5x + x2 = 0 + 5.583333333 2.5x + x2 = 0 + 5.583333333 Combine like terms: 0 + 5.583333333 = 5.583333333 2.5x + x2 = 5.583333333 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 5.583333333 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 5.583333333 + 1.5625 Combine like terms: 5.583333333 + 1.5625 = 7.145833333 1.5625 + 2.5x + x2 = 7.145833333 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 7.145833333 Calculate the square root of the right side: 2.673169155 Break this problem into two subproblems by setting (x + 1.25) equal to 2.673169155 and -2.673169155.Subproblem 1
x + 1.25 = 2.673169155 Simplifying x + 1.25 = 2.673169155 Reorder the terms: 1.25 + x = 2.673169155 Solving 1.25 + x = 2.673169155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.673169155 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.673169155 + -1.25 x = 2.673169155 + -1.25 Combine like terms: 2.673169155 + -1.25 = 1.423169155 x = 1.423169155 Simplifying x = 1.423169155Subproblem 2
x + 1.25 = -2.673169155 Simplifying x + 1.25 = -2.673169155 Reorder the terms: 1.25 + x = -2.673169155 Solving 1.25 + x = -2.673169155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.673169155 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.673169155 + -1.25 x = -2.673169155 + -1.25 Combine like terms: -2.673169155 + -1.25 = -3.923169155 x = -3.923169155 Simplifying x = -3.923169155Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.423169155, -3.923169155}
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