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Simplifying ((x + 7)(3x)) + (x * x) = 0 Reorder the terms: ((7 + x)(3x)) + (x * x) = 0 Remove parenthesis around (3x) ((7 + x) * 3x) + (x * x) = 0 Reorder the terms for easier multiplication: (3x(7 + x)) + (x * x) = 0 ((7 * 3x + x * 3x)) + (x * x) = 0 ((21x + 3x2)) + (x * x) = 0 (21x + 3x2) + (x * x) = 0 Remove parenthesis around (21x + 3x2) 21x + 3x2 + (x * x) = 0 Multiply x * x 21x + 3x2 + (x2) = 0 21x + 3x2 + x2 = 0 Combine like terms: 3x2 + x2 = 4x2 21x + 4x2 = 0 Solving 21x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(21 + 4x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(21 + 4x)' equal to zero and attempt to solve: Simplifying 21 + 4x = 0 Solving 21 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + 4x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 4x = 0 + -21 4x = 0 + -21 Combine like terms: 0 + -21 = -21 4x = -21 Divide each side by '4'. x = -5.25 Simplifying x = -5.25Solution
x = {0, -5.25}
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