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Simplifying 49x2 + -1 + (6x + -5)(7x + 1) = 0 Reorder the terms: 49x2 + -1 + (-5 + 6x)(7x + 1) = 0 Reorder the terms: 49x2 + -1 + (-5 + 6x)(1 + 7x) = 0 Multiply (-5 + 6x) * (1 + 7x) 49x2 + -1 + (-5(1 + 7x) + 6x * (1 + 7x)) = 0 49x2 + -1 + ((1 * -5 + 7x * -5) + 6x * (1 + 7x)) = 0 49x2 + -1 + ((-5 + -35x) + 6x * (1 + 7x)) = 0 49x2 + -1 + (-5 + -35x + (1 * 6x + 7x * 6x)) = 0 49x2 + -1 + (-5 + -35x + (6x + 42x2)) = 0 Combine like terms: -35x + 6x = -29x 49x2 + -1 + (-5 + -29x + 42x2) = 0 Reorder the terms: -1 + -5 + -29x + 49x2 + 42x2 = 0 Combine like terms: -1 + -5 = -6 -6 + -29x + 49x2 + 42x2 = 0 Combine like terms: 49x2 + 42x2 = 91x2 -6 + -29x + 91x2 = 0 Solving -6 + -29x + 91x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -7x)(6 + -13x) = 0Subproblem 1
Set the factor '(-1 + -7x)' equal to zero and attempt to solve: Simplifying -1 + -7x = 0 Solving -1 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -7x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7x = 0 + 1 -7x = 0 + 1 Combine like terms: 0 + 1 = 1 -7x = 1 Divide each side by '-7'. x = -0.1428571429 Simplifying x = -0.1428571429Subproblem 2
Set the factor '(6 + -13x)' equal to zero and attempt to solve: Simplifying 6 + -13x = 0 Solving 6 + -13x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -13x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -13x = 0 + -6 -13x = 0 + -6 Combine like terms: 0 + -6 = -6 -13x = -6 Divide each side by '-13'. x = 0.4615384615 Simplifying x = 0.4615384615Solution
x = {-0.1428571429, 0.4615384615}
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