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Simplifying -2x2 + 20x + 11 = 0 Reorder the terms: 11 + 20x + -2x2 = 0 Solving 11 + 20x + -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 + -10x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -10x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -10x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -10x + x2 = 0 + 5.5 -10x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -10x + x2 = 5.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 5.5 + 25 Reorder the terms: 25 + -10x + x2 = 5.5 + 25 Combine like terms: 5.5 + 25 = 30.5 25 + -10x + x2 = 30.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 30.5 Calculate the square root of the right side: 5.522680509 Break this problem into two subproblems by setting (x + -5) equal to 5.522680509 and -5.522680509.Subproblem 1
x + -5 = 5.522680509 Simplifying x + -5 = 5.522680509 Reorder the terms: -5 + x = 5.522680509 Solving -5 + x = 5.522680509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.522680509 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.522680509 + 5 x = 5.522680509 + 5 Combine like terms: 5.522680509 + 5 = 10.522680509 x = 10.522680509 Simplifying x = 10.522680509Subproblem 2
x + -5 = -5.522680509 Simplifying x + -5 = -5.522680509 Reorder the terms: -5 + x = -5.522680509 Solving -5 + x = -5.522680509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.522680509 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.522680509 + 5 x = -5.522680509 + 5 Combine like terms: -5.522680509 + 5 = -0.522680509 x = -0.522680509 Simplifying x = -0.522680509Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.522680509, -0.522680509}
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