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Simplifying (4x * x + -28x + 49) + -6(12x + -42)(x + -3) = 0 Multiply x * x (4x2 + -28x + 49) + -6(12x + -42)(x + -3) = 0 Reorder the terms: (49 + -28x + 4x2) + -6(12x + -42)(x + -3) = 0 Remove parenthesis around (49 + -28x + 4x2) 49 + -28x + 4x2 + -6(12x + -42)(x + -3) = 0 Reorder the terms: 49 + -28x + 4x2 + -6(-42 + 12x)(x + -3) = 0 Reorder the terms: 49 + -28x + 4x2 + -6(-42 + 12x)(-3 + x) = 0 Multiply (-42 + 12x) * (-3 + x) 49 + -28x + 4x2 + -6(-42(-3 + x) + 12x * (-3 + x)) = 0 49 + -28x + 4x2 + -6((-3 * -42 + x * -42) + 12x * (-3 + x)) = 0 49 + -28x + 4x2 + -6((126 + -42x) + 12x * (-3 + x)) = 0 49 + -28x + 4x2 + -6(126 + -42x + (-3 * 12x + x * 12x)) = 0 49 + -28x + 4x2 + -6(126 + -42x + (-36x + 12x2)) = 0 Combine like terms: -42x + -36x = -78x 49 + -28x + 4x2 + -6(126 + -78x + 12x2) = 0 49 + -28x + 4x2 + (126 * -6 + -78x * -6 + 12x2 * -6) = 0 49 + -28x + 4x2 + (-756 + 468x + -72x2) = 0 Reorder the terms: 49 + -756 + -28x + 468x + 4x2 + -72x2 = 0 Combine like terms: 49 + -756 = -707 -707 + -28x + 468x + 4x2 + -72x2 = 0 Combine like terms: -28x + 468x = 440x -707 + 440x + 4x2 + -72x2 = 0 Combine like terms: 4x2 + -72x2 = -68x2 -707 + 440x + -68x2 = 0 Solving -707 + 440x + -68x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + 2x)(101 + -34x) = 0Subproblem 1
Set the factor '(-7 + 2x)' equal to zero and attempt to solve: Simplifying -7 + 2x = 0 Solving -7 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2x = 0 + 7 2x = 0 + 7 Combine like terms: 0 + 7 = 7 2x = 7 Divide each side by '2'. x = 3.5 Simplifying x = 3.5Subproblem 2
Set the factor '(101 + -34x)' equal to zero and attempt to solve: Simplifying 101 + -34x = 0 Solving 101 + -34x = 0 Move all terms containing x to the left, all other terms to the right. Add '-101' to each side of the equation. 101 + -101 + -34x = 0 + -101 Combine like terms: 101 + -101 = 0 0 + -34x = 0 + -101 -34x = 0 + -101 Combine like terms: 0 + -101 = -101 -34x = -101 Divide each side by '-34'. x = 2.970588235 Simplifying x = 2.970588235Solution
x = {3.5, 2.970588235}
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