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Simplifying (3x + -5) + (1x + -7)(7x + 12) = 0 Reorder the terms: (-5 + 3x) + (1x + -7)(7x + 12) = 0 Remove parenthesis around (-5 + 3x) -5 + 3x + (1x + -7)(7x + 12) = 0 Reorder the terms: -5 + 3x + (-7 + 1x)(7x + 12) = 0 Reorder the terms: -5 + 3x + (-7 + 1x)(12 + 7x) = 0 Multiply (-7 + 1x) * (12 + 7x) -5 + 3x + (-7(12 + 7x) + 1x * (12 + 7x)) = 0 -5 + 3x + ((12 * -7 + 7x * -7) + 1x * (12 + 7x)) = 0 -5 + 3x + ((-84 + -49x) + 1x * (12 + 7x)) = 0 -5 + 3x + (-84 + -49x + (12 * 1x + 7x * 1x)) = 0 -5 + 3x + (-84 + -49x + (12x + 7x2)) = 0 Combine like terms: -49x + 12x = -37x -5 + 3x + (-84 + -37x + 7x2) = 0 Reorder the terms: -5 + -84 + 3x + -37x + 7x2 = 0 Combine like terms: -5 + -84 = -89 -89 + 3x + -37x + 7x2 = 0 Combine like terms: 3x + -37x = -34x -89 + -34x + 7x2 = 0 Solving -89 + -34x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -12.71428571 + -4.857142857x + x2 = 0 Move the constant term to the right: Add '12.71428571' to each side of the equation. -12.71428571 + -4.857142857x + 12.71428571 + x2 = 0 + 12.71428571 Reorder the terms: -12.71428571 + 12.71428571 + -4.857142857x + x2 = 0 + 12.71428571 Combine like terms: -12.71428571 + 12.71428571 = 0.00000000 0.00000000 + -4.857142857x + x2 = 0 + 12.71428571 -4.857142857x + x2 = 0 + 12.71428571 Combine like terms: 0 + 12.71428571 = 12.71428571 -4.857142857x + x2 = 12.71428571 The x term is -4.857142857x. Take half its coefficient (-2.428571429). Square it (5.897959186) and add it to both sides. Add '5.897959186' to each side of the equation. -4.857142857x + 5.897959186 + x2 = 12.71428571 + 5.897959186 Reorder the terms: 5.897959186 + -4.857142857x + x2 = 12.71428571 + 5.897959186 Combine like terms: 12.71428571 + 5.897959186 = 18.612244896 5.897959186 + -4.857142857x + x2 = 18.612244896 Factor a perfect square on the left side: (x + -2.428571429)(x + -2.428571429) = 18.612244896 Calculate the square root of the right side: 4.314191106 Break this problem into two subproblems by setting (x + -2.428571429) equal to 4.314191106 and -4.314191106.Subproblem 1
x + -2.428571429 = 4.314191106 Simplifying x + -2.428571429 = 4.314191106 Reorder the terms: -2.428571429 + x = 4.314191106 Solving -2.428571429 + x = 4.314191106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.428571429' to each side of the equation. -2.428571429 + 2.428571429 + x = 4.314191106 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + x = 4.314191106 + 2.428571429 x = 4.314191106 + 2.428571429 Combine like terms: 4.314191106 + 2.428571429 = 6.742762535 x = 6.742762535 Simplifying x = 6.742762535Subproblem 2
x + -2.428571429 = -4.314191106 Simplifying x + -2.428571429 = -4.314191106 Reorder the terms: -2.428571429 + x = -4.314191106 Solving -2.428571429 + x = -4.314191106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.428571429' to each side of the equation. -2.428571429 + 2.428571429 + x = -4.314191106 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + x = -4.314191106 + 2.428571429 x = -4.314191106 + 2.428571429 Combine like terms: -4.314191106 + 2.428571429 = -1.885619677 x = -1.885619677 Simplifying x = -1.885619677Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.742762535, -1.885619677}
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