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Simplifying 2x2 + 16x + -11 = 0 Reorder the terms: -11 + 16x + 2x2 = 0 Solving -11 + 16x + 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 + 8x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 8x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 8x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 8x + x2 = 0 + 5.5 8x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 8x + x2 = 5.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 5.5 + 16 Reorder the terms: 16 + 8x + x2 = 5.5 + 16 Combine like terms: 5.5 + 16 = 21.5 16 + 8x + x2 = 21.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 21.5 Calculate the square root of the right side: 4.636809248 Break this problem into two subproblems by setting (x + 4) equal to 4.636809248 and -4.636809248.Subproblem 1
x + 4 = 4.636809248 Simplifying x + 4 = 4.636809248 Reorder the terms: 4 + x = 4.636809248 Solving 4 + x = 4.636809248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.636809248 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.636809248 + -4 x = 4.636809248 + -4 Combine like terms: 4.636809248 + -4 = 0.636809248 x = 0.636809248 Simplifying x = 0.636809248Subproblem 2
x + 4 = -4.636809248 Simplifying x + 4 = -4.636809248 Reorder the terms: 4 + x = -4.636809248 Solving 4 + x = -4.636809248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.636809248 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.636809248 + -4 x = -4.636809248 + -4 Combine like terms: -4.636809248 + -4 = -8.636809248 x = -8.636809248 Simplifying x = -8.636809248Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.636809248, -8.636809248}
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