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Simplifying 2x(3 + 6x) = 5 (3 * 2x + 6x * 2x) = 5 (6x + 12x2) = 5 Solving 6x + 12x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 6x + 12x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 6x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.4166666667 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.5x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + 0.5x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + 0.4166666667 0.5x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 0.5x + x2 = 0.4166666667 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.4166666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.4166666667 + 0.0625 Combine like terms: 0.4166666667 + 0.0625 = 0.4791666667 0.0625 + 0.5x + x2 = 0.4791666667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.4791666667 Calculate the square root of the right side: 0.692218655 Break this problem into two subproblems by setting (x + 0.25) equal to 0.692218655 and -0.692218655.Subproblem 1
x + 0.25 = 0.692218655 Simplifying x + 0.25 = 0.692218655 Reorder the terms: 0.25 + x = 0.692218655 Solving 0.25 + x = 0.692218655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.692218655 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.692218655 + -0.25 x = 0.692218655 + -0.25 Combine like terms: 0.692218655 + -0.25 = 0.442218655 x = 0.442218655 Simplifying x = 0.442218655Subproblem 2
x + 0.25 = -0.692218655 Simplifying x + 0.25 = -0.692218655 Reorder the terms: 0.25 + x = -0.692218655 Solving 0.25 + x = -0.692218655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.692218655 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.692218655 + -0.25 x = -0.692218655 + -0.25 Combine like terms: -0.692218655 + -0.25 = -0.942218655 x = -0.942218655 Simplifying x = -0.942218655Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.442218655, -0.942218655}
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