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Simplifying (3x + 24)(3x) = 2 Reorder the terms: (24 + 3x)(3x) = 2 Remove parenthesis around (3x) (24 + 3x) * 3x = 2 Reorder the terms for easier multiplication: 3x(24 + 3x) = 2 (24 * 3x + 3x * 3x) = 2 (72x + 9x2) = 2 Solving 72x + 9x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 72x + 9x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 72x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + 8x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 8x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 8x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 8x + x2 = 0 + 0.2222222222 8x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 8x + x2 = 0.2222222222 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 0.2222222222 + 16 Reorder the terms: 16 + 8x + x2 = 0.2222222222 + 16 Combine like terms: 0.2222222222 + 16 = 16.2222222222 16 + 8x + x2 = 16.2222222222 Factor a perfect square on the left side: (x + 4)(x + 4) = 16.2222222222 Calculate the square root of the right side: 4.027681991 Break this problem into two subproblems by setting (x + 4) equal to 4.027681991 and -4.027681991.Subproblem 1
x + 4 = 4.027681991 Simplifying x + 4 = 4.027681991 Reorder the terms: 4 + x = 4.027681991 Solving 4 + x = 4.027681991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.027681991 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.027681991 + -4 x = 4.027681991 + -4 Combine like terms: 4.027681991 + -4 = 0.027681991 x = 0.027681991 Simplifying x = 0.027681991Subproblem 2
x + 4 = -4.027681991 Simplifying x + 4 = -4.027681991 Reorder the terms: 4 + x = -4.027681991 Solving 4 + x = -4.027681991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.027681991 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.027681991 + -4 x = -4.027681991 + -4 Combine like terms: -4.027681991 + -4 = -8.027681991 x = -8.027681991 Simplifying x = -8.027681991Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.027681991, -8.027681991}
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