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Simplifying 11x2 + 14x + -364 = 0 Reorder the terms: -364 + 14x + 11x2 = 0 Solving -364 + 14x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -33.09090909 + 1.272727273x + x2 = 0 Move the constant term to the right: Add '33.09090909' to each side of the equation. -33.09090909 + 1.272727273x + 33.09090909 + x2 = 0 + 33.09090909 Reorder the terms: -33.09090909 + 33.09090909 + 1.272727273x + x2 = 0 + 33.09090909 Combine like terms: -33.09090909 + 33.09090909 = 0.00000000 0.00000000 + 1.272727273x + x2 = 0 + 33.09090909 1.272727273x + x2 = 0 + 33.09090909 Combine like terms: 0 + 33.09090909 = 33.09090909 1.272727273x + x2 = 33.09090909 The x term is 1.272727273x. Take half its coefficient (0.6363636365). Square it (0.4049586779) and add it to both sides. Add '0.4049586779' to each side of the equation. 1.272727273x + 0.4049586779 + x2 = 33.09090909 + 0.4049586779 Reorder the terms: 0.4049586779 + 1.272727273x + x2 = 33.09090909 + 0.4049586779 Combine like terms: 33.09090909 + 0.4049586779 = 33.4958677679 0.4049586779 + 1.272727273x + x2 = 33.4958677679 Factor a perfect square on the left side: (x + 0.6363636365)(x + 0.6363636365) = 33.4958677679 Calculate the square root of the right side: 5.78756147 Break this problem into two subproblems by setting (x + 0.6363636365) equal to 5.78756147 and -5.78756147.Subproblem 1
x + 0.6363636365 = 5.78756147 Simplifying x + 0.6363636365 = 5.78756147 Reorder the terms: 0.6363636365 + x = 5.78756147 Solving 0.6363636365 + x = 5.78756147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6363636365' to each side of the equation. 0.6363636365 + -0.6363636365 + x = 5.78756147 + -0.6363636365 Combine like terms: 0.6363636365 + -0.6363636365 = 0.0000000000 0.0000000000 + x = 5.78756147 + -0.6363636365 x = 5.78756147 + -0.6363636365 Combine like terms: 5.78756147 + -0.6363636365 = 5.1511978335 x = 5.1511978335 Simplifying x = 5.1511978335Subproblem 2
x + 0.6363636365 = -5.78756147 Simplifying x + 0.6363636365 = -5.78756147 Reorder the terms: 0.6363636365 + x = -5.78756147 Solving 0.6363636365 + x = -5.78756147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6363636365' to each side of the equation. 0.6363636365 + -0.6363636365 + x = -5.78756147 + -0.6363636365 Combine like terms: 0.6363636365 + -0.6363636365 = 0.0000000000 0.0000000000 + x = -5.78756147 + -0.6363636365 x = -5.78756147 + -0.6363636365 Combine like terms: -5.78756147 + -0.6363636365 = -6.4239251065 x = -6.4239251065 Simplifying x = -6.4239251065Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.1511978335, -6.4239251065}
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