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Simplifying (3x + -5)(7 + 6x) + -1(7 + x) = 0 Reorder the terms: (-5 + 3x)(7 + 6x) + -1(7 + x) = 0 Multiply (-5 + 3x) * (7 + 6x) (-5(7 + 6x) + 3x * (7 + 6x)) + -1(7 + x) = 0 ((7 * -5 + 6x * -5) + 3x * (7 + 6x)) + -1(7 + x) = 0 ((-35 + -30x) + 3x * (7 + 6x)) + -1(7 + x) = 0 (-35 + -30x + (7 * 3x + 6x * 3x)) + -1(7 + x) = 0 (-35 + -30x + (21x + 18x2)) + -1(7 + x) = 0 Combine like terms: -30x + 21x = -9x (-35 + -9x + 18x2) + -1(7 + x) = 0 -35 + -9x + 18x2 + (7 * -1 + x * -1) = 0 -35 + -9x + 18x2 + (-7 + -1x) = 0 Reorder the terms: -35 + -7 + -9x + -1x + 18x2 = 0 Combine like terms: -35 + -7 = -42 -42 + -9x + -1x + 18x2 = 0 Combine like terms: -9x + -1x = -10x -42 + -10x + 18x2 = 0 Solving -42 + -10x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -5x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -5x + 9x2)' equal to zero and attempt to solve: Simplifying -21 + -5x + 9x2 = 0 Solving -21 + -5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.333333333 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -0.5555555556x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -0.5555555556x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -0.5555555556x + x2 = 0 + 2.333333333 -0.5555555556x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -0.5555555556x + x2 = 2.333333333 The x term is -0.5555555556x. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556x + 0.07716049384 + x2 = 2.333333333 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 2.333333333 + 0.07716049384 Combine like terms: 2.333333333 + 0.07716049384 = 2.41049382684 0.07716049384 + -0.5555555556x + x2 = 2.41049382684 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 2.41049382684 Calculate the square root of the right side: 1.552576512 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 1.552576512 and -1.552576512.Subproblem 1
x + -0.2777777778 = 1.552576512 Simplifying x + -0.2777777778 = 1.552576512 Reorder the terms: -0.2777777778 + x = 1.552576512 Solving -0.2777777778 + x = 1.552576512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = 1.552576512 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 1.552576512 + 0.2777777778 x = 1.552576512 + 0.2777777778 Combine like terms: 1.552576512 + 0.2777777778 = 1.8303542898 x = 1.8303542898 Simplifying x = 1.8303542898Subproblem 2
x + -0.2777777778 = -1.552576512 Simplifying x + -0.2777777778 = -1.552576512 Reorder the terms: -0.2777777778 + x = -1.552576512 Solving -0.2777777778 + x = -1.552576512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = -1.552576512 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -1.552576512 + 0.2777777778 x = -1.552576512 + 0.2777777778 Combine like terms: -1.552576512 + 0.2777777778 = -1.2747987342 x = -1.2747987342 Simplifying x = -1.2747987342Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8303542898, -1.2747987342}Solution
x = {1.8303542898, -1.2747987342}
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