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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 = 6.150367627 x = 6.150367627 Simplifying x = 6.150367627Subproblem 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 = -0.650367627 x = -0.650367627 Simplifying x = -0.650367627Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.150367627, -0.650367627}
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