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Simplifying (15x + 8)(x + -1) = 6 Reorder the terms: (8 + 15x)(x + -1) = 6 Reorder the terms: (8 + 15x)(-1 + x) = 6 Multiply (8 + 15x) * (-1 + x) (8(-1 + x) + 15x * (-1 + x)) = 6 ((-1 * 8 + x * 8) + 15x * (-1 + x)) = 6 ((-8 + 8x) + 15x * (-1 + x)) = 6 (-8 + 8x + (-1 * 15x + x * 15x)) = 6 (-8 + 8x + (-15x + 15x2)) = 6 Combine like terms: 8x + -15x = -7x (-8 + -7x + 15x2) = 6 Solving -8 + -7x + 15x2 = 6 Solving for variable 'x'. Reorder the terms: -8 + -6 + -7x + 15x2 = 6 + -6 Combine like terms: -8 + -6 = -14 -14 + -7x + 15x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -14 + -7x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.9333333333 + -0.4666666667x + x2 = 0 Move the constant term to the right: Add '0.9333333333' to each side of the equation. -0.9333333333 + -0.4666666667x + 0.9333333333 + x2 = 0 + 0.9333333333 Reorder the terms: -0.9333333333 + 0.9333333333 + -0.4666666667x + x2 = 0 + 0.9333333333 Combine like terms: -0.9333333333 + 0.9333333333 = 0.0000000000 0.0000000000 + -0.4666666667x + x2 = 0 + 0.9333333333 -0.4666666667x + x2 = 0 + 0.9333333333 Combine like terms: 0 + 0.9333333333 = 0.9333333333 -0.4666666667x + x2 = 0.9333333333 The x term is -0.4666666667x. Take half its coefficient (-0.2333333334). Square it (0.05444444448) and add it to both sides. Add '0.05444444448' to each side of the equation. -0.4666666667x + 0.05444444448 + x2 = 0.9333333333 + 0.05444444448 Reorder the terms: 0.05444444448 + -0.4666666667x + x2 = 0.9333333333 + 0.05444444448 Combine like terms: 0.9333333333 + 0.05444444448 = 0.98777777778 0.05444444448 + -0.4666666667x + x2 = 0.98777777778 Factor a perfect square on the left side: (x + -0.2333333334)(x + -0.2333333334) = 0.98777777778 Calculate the square root of the right side: 0.993870101 Break this problem into two subproblems by setting (x + -0.2333333334) equal to 0.993870101 and -0.993870101.Subproblem 1
x + -0.2333333334 = 0.993870101 Simplifying x + -0.2333333334 = 0.993870101 Reorder the terms: -0.2333333334 + x = 0.993870101 Solving -0.2333333334 + x = 0.993870101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + x = 0.993870101 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + x = 0.993870101 + 0.2333333334 x = 0.993870101 + 0.2333333334 Combine like terms: 0.993870101 + 0.2333333334 = 1.2272034344 x = 1.2272034344 Simplifying x = 1.2272034344Subproblem 2
x + -0.2333333334 = -0.993870101 Simplifying x + -0.2333333334 = -0.993870101 Reorder the terms: -0.2333333334 + x = -0.993870101 Solving -0.2333333334 + x = -0.993870101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + x = -0.993870101 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + x = -0.993870101 + 0.2333333334 x = -0.993870101 + 0.2333333334 Combine like terms: -0.993870101 + 0.2333333334 = -0.7605367676 x = -0.7605367676 Simplifying x = -0.7605367676Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2272034344, -0.7605367676}
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