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Simplifying (6x + -8)(2x + 7) + -3(3 + -1x) = 0 Reorder the terms: (-8 + 6x)(2x + 7) + -3(3 + -1x) = 0 Reorder the terms: (-8 + 6x)(7 + 2x) + -3(3 + -1x) = 0 Multiply (-8 + 6x) * (7 + 2x) (-8(7 + 2x) + 6x * (7 + 2x)) + -3(3 + -1x) = 0 ((7 * -8 + 2x * -8) + 6x * (7 + 2x)) + -3(3 + -1x) = 0 ((-56 + -16x) + 6x * (7 + 2x)) + -3(3 + -1x) = 0 (-56 + -16x + (7 * 6x + 2x * 6x)) + -3(3 + -1x) = 0 (-56 + -16x + (42x + 12x2)) + -3(3 + -1x) = 0 Combine like terms: -16x + 42x = 26x (-56 + 26x + 12x2) + -3(3 + -1x) = 0 -56 + 26x + 12x2 + (3 * -3 + -1x * -3) = 0 -56 + 26x + 12x2 + (-9 + 3x) = 0 Reorder the terms: -56 + -9 + 26x + 3x + 12x2 = 0 Combine like terms: -56 + -9 = -65 -65 + 26x + 3x + 12x2 = 0 Combine like terms: 26x + 3x = 29x -65 + 29x + 12x2 = 0 Solving -65 + 29x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -5.416666667 + 2.416666667x + x2 = 0 Move the constant term to the right: Add '5.416666667' to each side of the equation. -5.416666667 + 2.416666667x + 5.416666667 + x2 = 0 + 5.416666667 Reorder the terms: -5.416666667 + 5.416666667 + 2.416666667x + x2 = 0 + 5.416666667 Combine like terms: -5.416666667 + 5.416666667 = 0.000000000 0.000000000 + 2.416666667x + x2 = 0 + 5.416666667 2.416666667x + x2 = 0 + 5.416666667 Combine like terms: 0 + 5.416666667 = 5.416666667 2.416666667x + x2 = 5.416666667 The x term is 2.416666667x. Take half its coefficient (1.208333334). Square it (1.460069446) and add it to both sides. Add '1.460069446' to each side of the equation. 2.416666667x + 1.460069446 + x2 = 5.416666667 + 1.460069446 Reorder the terms: 1.460069446 + 2.416666667x + x2 = 5.416666667 + 1.460069446 Combine like terms: 5.416666667 + 1.460069446 = 6.876736113 1.460069446 + 2.416666667x + x2 = 6.876736113 Factor a perfect square on the left side: (x + 1.208333334)(x + 1.208333334) = 6.876736113 Calculate the square root of the right side: 2.622353163 Break this problem into two subproblems by setting (x + 1.208333334) equal to 2.622353163 and -2.622353163.Subproblem 1
x + 1.208333334 = 2.622353163 Simplifying x + 1.208333334 = 2.622353163 Reorder the terms: 1.208333334 + x = 2.622353163 Solving 1.208333334 + x = 2.622353163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.208333334' to each side of the equation. 1.208333334 + -1.208333334 + x = 2.622353163 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + x = 2.622353163 + -1.208333334 x = 2.622353163 + -1.208333334 Combine like terms: 2.622353163 + -1.208333334 = 1.414019829 x = 1.414019829 Simplifying x = 1.414019829Subproblem 2
x + 1.208333334 = -2.622353163 Simplifying x + 1.208333334 = -2.622353163 Reorder the terms: 1.208333334 + x = -2.622353163 Solving 1.208333334 + x = -2.622353163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.208333334' to each side of the equation. 1.208333334 + -1.208333334 + x = -2.622353163 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + x = -2.622353163 + -1.208333334 x = -2.622353163 + -1.208333334 Combine like terms: -2.622353163 + -1.208333334 = -3.830686497 x = -3.830686497 Simplifying x = -3.830686497Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.414019829, -3.830686497}
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