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Simplifying 49x2 + 14x + 1 + -1(7x + 1)(3x + -50) = 0 Reorder the terms: 49x2 + 14x + 1 + -1(1 + 7x)(3x + -50) = 0 Reorder the terms: 49x2 + 14x + 1 + -1(1 + 7x)(-50 + 3x) = 0 Multiply (1 + 7x) * (-50 + 3x) 49x2 + 14x + 1 + -1(1(-50 + 3x) + 7x * (-50 + 3x)) = 0 49x2 + 14x + 1 + -1((-50 * 1 + 3x * 1) + 7x * (-50 + 3x)) = 0 49x2 + 14x + 1 + -1((-50 + 3x) + 7x * (-50 + 3x)) = 0 49x2 + 14x + 1 + -1(-50 + 3x + (-50 * 7x + 3x * 7x)) = 0 49x2 + 14x + 1 + -1(-50 + 3x + (-350x + 21x2)) = 0 Combine like terms: 3x + -350x = -347x 49x2 + 14x + 1 + -1(-50 + -347x + 21x2) = 0 49x2 + 14x + 1 + (-50 * -1 + -347x * -1 + 21x2 * -1) = 0 49x2 + 14x + 1 + (50 + 347x + -21x2) = 0 Reorder the terms: 1 + 50 + 14x + 347x + 49x2 + -21x2 = 0 Combine like terms: 1 + 50 = 51 51 + 14x + 347x + 49x2 + -21x2 = 0 Combine like terms: 14x + 347x = 361x 51 + 361x + 49x2 + -21x2 = 0 Combine like terms: 49x2 + -21x2 = 28x2 51 + 361x + 28x2 = 0 Solving 51 + 361x + 28x2 = 0 Solving for variable 'x'. Factor a trinomial. (51 + 4x)(1 + 7x) = 0Subproblem 1
Set the factor '(51 + 4x)' equal to zero and attempt to solve: Simplifying 51 + 4x = 0 Solving 51 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-51' to each side of the equation. 51 + -51 + 4x = 0 + -51 Combine like terms: 51 + -51 = 0 0 + 4x = 0 + -51 4x = 0 + -51 Combine like terms: 0 + -51 = -51 4x = -51 Divide each side by '4'. x = -12.75 Simplifying x = -12.75Subproblem 2
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 = -0.1428571429Solution
x = {-12.75, -0.1428571429}
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