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Simplifying 2x(6 + x) = 19 (6 * 2x + x * 2x) = 19 (12x + 2x2) = 19 Solving 12x + 2x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + 12x + 2x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + 6x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 6x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 6x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 6x + x2 = 0 + 9.5 6x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 6x + x2 = 9.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 9.5 + 9 Reorder the terms: 9 + 6x + x2 = 9.5 + 9 Combine like terms: 9.5 + 9 = 18.5 9 + 6x + x2 = 18.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 18.5 Calculate the square root of the right side: 4.301162634 Break this problem into two subproblems by setting (x + 3) equal to 4.301162634 and -4.301162634.Subproblem 1
x + 3 = 4.301162634 Simplifying x + 3 = 4.301162634 Reorder the terms: 3 + x = 4.301162634 Solving 3 + x = 4.301162634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.301162634 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.301162634 + -3 x = 4.301162634 + -3 Combine like terms: 4.301162634 + -3 = 1.301162634 x = 1.301162634 Simplifying x = 1.301162634Subproblem 2
x + 3 = -4.301162634 Simplifying x + 3 = -4.301162634 Reorder the terms: 3 + x = -4.301162634 Solving 3 + x = -4.301162634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.301162634 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.301162634 + -3 x = -4.301162634 + -3 Combine like terms: -4.301162634 + -3 = -7.301162634 x = -7.301162634 Simplifying x = -7.301162634Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.301162634, -7.301162634}
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