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Simplifying 396 = x2 + 11x Reorder the terms: 396 = 11x + x2 Solving 396 = 11x + x2 Solving for variable 'x'. Reorder the terms: 396 + -11x + -1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 396 + -11x + -1x2 = 0 + x2 + -1x2 396 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 396 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -396 + 11x + x2 = 0 Move the constant term to the right: Add '396' to each side of the equation. -396 + 11x + 396 + x2 = 0 + 396 Reorder the terms: -396 + 396 + 11x + x2 = 0 + 396 Combine like terms: -396 + 396 = 0 0 + 11x + x2 = 0 + 396 11x + x2 = 0 + 396 Combine like terms: 0 + 396 = 396 11x + x2 = 396 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 396 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 396 + 30.25 Combine like terms: 396 + 30.25 = 426.25 30.25 + 11x + x2 = 426.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 426.25 Calculate the square root of the right side: 20.645822822 Break this problem into two subproblems by setting (x + 5.5) equal to 20.645822822 and -20.645822822.Subproblem 1
x + 5.5 = 20.645822822 Simplifying x + 5.5 = 20.645822822 Reorder the terms: 5.5 + x = 20.645822822 Solving 5.5 + x = 20.645822822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 20.645822822 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 20.645822822 + -5.5 x = 20.645822822 + -5.5 Combine like terms: 20.645822822 + -5.5 = 15.145822822 x = 15.145822822 Simplifying x = 15.145822822Subproblem 2
x + 5.5 = -20.645822822 Simplifying x + 5.5 = -20.645822822 Reorder the terms: 5.5 + x = -20.645822822 Solving 5.5 + x = -20.645822822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -20.645822822 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -20.645822822 + -5.5 x = -20.645822822 + -5.5 Combine like terms: -20.645822822 + -5.5 = -26.145822822 x = -26.145822822 Simplifying x = -26.145822822Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.145822822, -26.145822822}
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