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Simplifying 6x(x + 3) = 6x + 11 Reorder the terms: 6x(3 + x) = 6x + 11 (3 * 6x + x * 6x) = 6x + 11 (18x + 6x2) = 6x + 11 Reorder the terms: 18x + 6x2 = 11 + 6x Solving 18x + 6x2 = 11 + 6x Solving for variable 'x'. Reorder the terms: -11 + 18x + -6x + 6x2 = 11 + 6x + -11 + -6x Combine like terms: 18x + -6x = 12x -11 + 12x + 6x2 = 11 + 6x + -11 + -6x Reorder the terms: -11 + 12x + 6x2 = 11 + -11 + 6x + -6x Combine like terms: 11 + -11 = 0 -11 + 12x + 6x2 = 0 + 6x + -6x -11 + 12x + 6x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -11 + 12x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + 2x + x2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + 2x + 1.833333333 + x2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + 2x + x2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + 2x + x2 = 0 + 1.833333333 2x + x2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 2x + x2 = 1.833333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1.833333333 + 1 Reorder the terms: 1 + 2x + x2 = 1.833333333 + 1 Combine like terms: 1.833333333 + 1 = 2.833333333 1 + 2x + x2 = 2.833333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.833333333 Calculate the square root of the right side: 1.683250823 Break this problem into two subproblems by setting (x + 1) equal to 1.683250823 and -1.683250823.Subproblem 1
x + 1 = 1.683250823 Simplifying x + 1 = 1.683250823 Reorder the terms: 1 + x = 1.683250823 Solving 1 + x = 1.683250823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.683250823 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.683250823 + -1 x = 1.683250823 + -1 Combine like terms: 1.683250823 + -1 = 0.683250823 x = 0.683250823 Simplifying x = 0.683250823Subproblem 2
x + 1 = -1.683250823 Simplifying x + 1 = -1.683250823 Reorder the terms: 1 + x = -1.683250823 Solving 1 + x = -1.683250823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.683250823 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.683250823 + -1 x = -1.683250823 + -1 Combine like terms: -1.683250823 + -1 = -2.683250823 x = -2.683250823 Simplifying x = -2.683250823Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.683250823, -2.683250823}
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