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Simplifying 2x2 + 14x + -11 = 0 Reorder the terms: -11 + 14x + 2x2 = 0 Solving -11 + 14x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 7x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 7x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 7x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 7x + x2 = 0 + 5.5 7x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 7x + x2 = 5.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 5.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 5.5 + 12.25 Combine like terms: 5.5 + 12.25 = 17.75 12.25 + 7x + x2 = 17.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (x + 3.5) equal to 4.213074887 and -4.213074887.Subproblem 1
x + 3.5 = 4.213074887 Simplifying x + 3.5 = 4.213074887 Reorder the terms: 3.5 + x = 4.213074887 Solving 3.5 + x = 4.213074887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.213074887 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.213074887 + -3.5 x = 4.213074887 + -3.5 Combine like terms: 4.213074887 + -3.5 = 0.713074887 x = 0.713074887 Simplifying x = 0.713074887Subproblem 2
x + 3.5 = -4.213074887 Simplifying x + 3.5 = -4.213074887 Reorder the terms: 3.5 + x = -4.213074887 Solving 3.5 + x = -4.213074887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.213074887 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.213074887 + -3.5 x = -4.213074887 + -3.5 Combine like terms: -4.213074887 + -3.5 = -7.713074887 x = -7.713074887 Simplifying x = -7.713074887Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.713074887, -7.713074887}
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