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Simplifying 20x2 + -215x = 11 Reorder the terms: -215x + 20x2 = 11 Solving -215x + 20x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -215x + 20x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -215x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.55 + -10.75x + x2 = 0 Move the constant term to the right: Add '0.55' to each side of the equation. -0.55 + -10.75x + 0.55 + x2 = 0 + 0.55 Reorder the terms: -0.55 + 0.55 + -10.75x + x2 = 0 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + -10.75x + x2 = 0 + 0.55 -10.75x + x2 = 0 + 0.55 Combine like terms: 0 + 0.55 = 0.55 -10.75x + x2 = 0.55 The x term is -10.75x. Take half its coefficient (-5.375). Square it (28.890625) and add it to both sides. Add '28.890625' to each side of the equation. -10.75x + 28.890625 + x2 = 0.55 + 28.890625 Reorder the terms: 28.890625 + -10.75x + x2 = 0.55 + 28.890625 Combine like terms: 0.55 + 28.890625 = 29.440625 28.890625 + -10.75x + x2 = 29.440625 Factor a perfect square on the left side: (x + -5.375)(x + -5.375) = 29.440625 Calculate the square root of the right side: 5.425921581 Break this problem into two subproblems by setting (x + -5.375) equal to 5.425921581 and -5.425921581.Subproblem 1
x + -5.375 = 5.425921581 Simplifying x + -5.375 = 5.425921581 Reorder the terms: -5.375 + x = 5.425921581 Solving -5.375 + x = 5.425921581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.375' to each side of the equation. -5.375 + 5.375 + x = 5.425921581 + 5.375 Combine like terms: -5.375 + 5.375 = 0.000 0.000 + x = 5.425921581 + 5.375 x = 5.425921581 + 5.375 Combine like terms: 5.425921581 + 5.375 = 10.800921581 x = 10.800921581 Simplifying x = 10.800921581Subproblem 2
x + -5.375 = -5.425921581 Simplifying x + -5.375 = -5.425921581 Reorder the terms: -5.375 + x = -5.425921581 Solving -5.375 + x = -5.425921581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.375' to each side of the equation. -5.375 + 5.375 + x = -5.425921581 + 5.375 Combine like terms: -5.375 + 5.375 = 0.000 0.000 + x = -5.425921581 + 5.375 x = -5.425921581 + 5.375 Combine like terms: -5.425921581 + 5.375 = -0.050921581 x = -0.050921581 Simplifying x = -0.050921581Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.800921581, -0.050921581}
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