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Simplifying 3x(x + 12) = 5 Reorder the terms: 3x(12 + x) = 5 (12 * 3x + x * 3x) = 5 (36x + 3x2) = 5 Solving 36x + 3x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 36x + 3x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 36x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + 12x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 12x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 12x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 12x + x2 = 0 + 1.666666667 12x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 12x + x2 = 1.666666667 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 1.666666667 + 36 Reorder the terms: 36 + 12x + x2 = 1.666666667 + 36 Combine like terms: 1.666666667 + 36 = 37.666666667 36 + 12x + x2 = 37.666666667 Factor a perfect square on the left side: (x + 6)(x + 6) = 37.666666667 Calculate the square root of the right side: 6.137317547 Break this problem into two subproblems by setting (x + 6) equal to 6.137317547 and -6.137317547.Subproblem 1
x + 6 = 6.137317547 Simplifying x + 6 = 6.137317547 Reorder the terms: 6 + x = 6.137317547 Solving 6 + x = 6.137317547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.137317547 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.137317547 + -6 x = 6.137317547 + -6 Combine like terms: 6.137317547 + -6 = 0.137317547 x = 0.137317547 Simplifying x = 0.137317547Subproblem 2
x + 6 = -6.137317547 Simplifying x + 6 = -6.137317547 Reorder the terms: 6 + x = -6.137317547 Solving 6 + x = -6.137317547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.137317547 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.137317547 + -6 x = -6.137317547 + -6 Combine like terms: -6.137317547 + -6 = -12.137317547 x = -12.137317547 Simplifying x = -12.137317547Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.137317547, -12.137317547}
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