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Simplifying 2x2 + 23x + -91 = 0 Reorder the terms: -91 + 23x + 2x2 = 0 Solving -91 + 23x + 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'. -45.5 + 11.5x + x2 = 0 Move the constant term to the right: Add '45.5' to each side of the equation. -45.5 + 11.5x + 45.5 + x2 = 0 + 45.5 Reorder the terms: -45.5 + 45.5 + 11.5x + x2 = 0 + 45.5 Combine like terms: -45.5 + 45.5 = 0.0 0.0 + 11.5x + x2 = 0 + 45.5 11.5x + x2 = 0 + 45.5 Combine like terms: 0 + 45.5 = 45.5 11.5x + x2 = 45.5 The x term is 11.5x. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5x + 33.0625 + x2 = 45.5 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = 45.5 + 33.0625 Combine like terms: 45.5 + 33.0625 = 78.5625 33.0625 + 11.5x + x2 = 78.5625 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = 78.5625 Calculate the square root of the right side: 8.863548951 Break this problem into two subproblems by setting (x + 5.75) equal to 8.863548951 and -8.863548951.Subproblem 1
x + 5.75 = 8.863548951 Simplifying x + 5.75 = 8.863548951 Reorder the terms: 5.75 + x = 8.863548951 Solving 5.75 + x = 8.863548951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 8.863548951 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 8.863548951 + -5.75 x = 8.863548951 + -5.75 Combine like terms: 8.863548951 + -5.75 = 3.113548951 x = 3.113548951 Simplifying x = 3.113548951Subproblem 2
x + 5.75 = -8.863548951 Simplifying x + 5.75 = -8.863548951 Reorder the terms: 5.75 + x = -8.863548951 Solving 5.75 + x = -8.863548951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -8.863548951 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -8.863548951 + -5.75 x = -8.863548951 + -5.75 Combine like terms: -8.863548951 + -5.75 = -14.613548951 x = -14.613548951 Simplifying x = -14.613548951Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.113548951, -14.613548951}
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