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Simplifying (7x + 1)(12x + -9) + -1(-1x + 2) = 0 Reorder the terms: (1 + 7x)(12x + -9) + -1(-1x + 2) = 0 Reorder the terms: (1 + 7x)(-9 + 12x) + -1(-1x + 2) = 0 Multiply (1 + 7x) * (-9 + 12x) (1(-9 + 12x) + 7x * (-9 + 12x)) + -1(-1x + 2) = 0 ((-9 * 1 + 12x * 1) + 7x * (-9 + 12x)) + -1(-1x + 2) = 0 ((-9 + 12x) + 7x * (-9 + 12x)) + -1(-1x + 2) = 0 (-9 + 12x + (-9 * 7x + 12x * 7x)) + -1(-1x + 2) = 0 (-9 + 12x + (-63x + 84x2)) + -1(-1x + 2) = 0 Combine like terms: 12x + -63x = -51x (-9 + -51x + 84x2) + -1(-1x + 2) = 0 Reorder the terms: -9 + -51x + 84x2 + -1(2 + -1x) = 0 -9 + -51x + 84x2 + (2 * -1 + -1x * -1) = 0 -9 + -51x + 84x2 + (-2 + 1x) = 0 Reorder the terms: -9 + -2 + -51x + 1x + 84x2 = 0 Combine like terms: -9 + -2 = -11 -11 + -51x + 1x + 84x2 = 0 Combine like terms: -51x + 1x = -50x -11 + -50x + 84x2 = 0 Solving -11 + -50x + 84x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 84 the coefficient of the squared term: Divide each side by '84'. -0.130952381 + -0.5952380952x + x2 = 0 Move the constant term to the right: Add '0.130952381' to each side of the equation. -0.130952381 + -0.5952380952x + 0.130952381 + x2 = 0 + 0.130952381 Reorder the terms: -0.130952381 + 0.130952381 + -0.5952380952x + x2 = 0 + 0.130952381 Combine like terms: -0.130952381 + 0.130952381 = 0.000000000 0.000000000 + -0.5952380952x + x2 = 0 + 0.130952381 -0.5952380952x + x2 = 0 + 0.130952381 Combine like terms: 0 + 0.130952381 = 0.130952381 -0.5952380952x + x2 = 0.130952381 The x term is -0.5952380952x. Take half its coefficient (-0.2976190476). Square it (0.08857709749) and add it to both sides. Add '0.08857709749' to each side of the equation. -0.5952380952x + 0.08857709749 + x2 = 0.130952381 + 0.08857709749 Reorder the terms: 0.08857709749 + -0.5952380952x + x2 = 0.130952381 + 0.08857709749 Combine like terms: 0.130952381 + 0.08857709749 = 0.21952947849 0.08857709749 + -0.5952380952x + x2 = 0.21952947849 Factor a perfect square on the left side: (x + -0.2976190476)(x + -0.2976190476) = 0.21952947849 Calculate the square root of the right side: 0.46853973 Break this problem into two subproblems by setting (x + -0.2976190476) equal to 0.46853973 and -0.46853973.Subproblem 1
x + -0.2976190476 = 0.46853973 Simplifying x + -0.2976190476 = 0.46853973 Reorder the terms: -0.2976190476 + x = 0.46853973 Solving -0.2976190476 + x = 0.46853973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2976190476' to each side of the equation. -0.2976190476 + 0.2976190476 + x = 0.46853973 + 0.2976190476 Combine like terms: -0.2976190476 + 0.2976190476 = 0.0000000000 0.0000000000 + x = 0.46853973 + 0.2976190476 x = 0.46853973 + 0.2976190476 Combine like terms: 0.46853973 + 0.2976190476 = 0.7661587776 x = 0.7661587776 Simplifying x = 0.7661587776Subproblem 2
x + -0.2976190476 = -0.46853973 Simplifying x + -0.2976190476 = -0.46853973 Reorder the terms: -0.2976190476 + x = -0.46853973 Solving -0.2976190476 + x = -0.46853973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2976190476' to each side of the equation. -0.2976190476 + 0.2976190476 + x = -0.46853973 + 0.2976190476 Combine like terms: -0.2976190476 + 0.2976190476 = 0.0000000000 0.0000000000 + x = -0.46853973 + 0.2976190476 x = -0.46853973 + 0.2976190476 Combine like terms: -0.46853973 + 0.2976190476 = -0.1709206824 x = -0.1709206824 Simplifying x = -0.1709206824Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7661587776, -0.1709206824}
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