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Simplifying 2x2 + 11x + -8 = 0 Reorder the terms: -8 + 11x + 2x2 = 0 Solving -8 + 11x + 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'. -4 + 5.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 5.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 5.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5.5x + x2 = 0 + 4 5.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 5.5x + x2 = 4 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 4 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 4 + 7.5625 Combine like terms: 4 + 7.5625 = 11.5625 7.5625 + 5.5x + x2 = 11.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (x + 2.75) equal to 3.400367627 and -3.400367627.Subproblem 1
x + 2.75 = 3.400367627 Simplifying x + 2.75 = 3.400367627 Reorder the terms: 2.75 + x = 3.400367627 Solving 2.75 + x = 3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 3.400367627 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 3.400367627 + -2.75 x = 3.400367627 + -2.75 Combine like terms: 3.400367627 + -2.75 = 0.650367627 x = 0.650367627 Simplifying x = 0.650367627Subproblem 2
x + 2.75 = -3.400367627 Simplifying x + 2.75 = -3.400367627 Reorder the terms: 2.75 + x = -3.400367627 Solving 2.75 + x = -3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -3.400367627 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -3.400367627 + -2.75 x = -3.400367627 + -2.75 Combine like terms: -3.400367627 + -2.75 = -6.150367627 x = -6.150367627 Simplifying x = -6.150367627Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.650367627, -6.150367627}
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