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Simplifying 2X2 + 8X + 9 = 20 Reorder the terms: 9 + 8X + 2X2 = 20 Solving 9 + 8X + 2X2 = 20 Solving for variable 'X'. Reorder the terms: 9 + -20 + 8X + 2X2 = 20 + -20 Combine like terms: 9 + -20 = -11 -11 + 8X + 2X2 = 20 + -20 Combine like terms: 20 + -20 = 0 -11 + 8X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 4X + X2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 4X + 5.5 + X2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 4X + X2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 4X + X2 = 0 + 5.5 4X + X2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 4X + X2 = 5.5 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = 5.5 + 4 Reorder the terms: 4 + 4X + X2 = 5.5 + 4 Combine like terms: 5.5 + 4 = 9.5 4 + 4X + X2 = 9.5 Factor a perfect square on the left side: (X + 2)(X + 2) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (X + 2) equal to 3.082207001 and -3.082207001.Subproblem 1
X + 2 = 3.082207001 Simplifying X + 2 = 3.082207001 Reorder the terms: 2 + X = 3.082207001 Solving 2 + X = 3.082207001 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 3.082207001 + -2 Combine like terms: 2 + -2 = 0 0 + X = 3.082207001 + -2 X = 3.082207001 + -2 Combine like terms: 3.082207001 + -2 = 1.082207001 X = 1.082207001 Simplifying X = 1.082207001Subproblem 2
X + 2 = -3.082207001 Simplifying X + 2 = -3.082207001 Reorder the terms: 2 + X = -3.082207001 Solving 2 + X = -3.082207001 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -3.082207001 + -2 Combine like terms: 2 + -2 = 0 0 + X = -3.082207001 + -2 X = -3.082207001 + -2 Combine like terms: -3.082207001 + -2 = -5.082207001 X = -5.082207001 Simplifying X = -5.082207001Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.082207001, -5.082207001}
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