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Simplifying 2X2 + -22X + 49 = 0 Reorder the terms: 49 + -22X + 2X2 = 0 Solving 49 + -22X + 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'. 24.5 + -11X + X2 = 0 Move the constant term to the right: Add '-24.5' to each side of the equation. 24.5 + -11X + -24.5 + X2 = 0 + -24.5 Reorder the terms: 24.5 + -24.5 + -11X + X2 = 0 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + -11X + X2 = 0 + -24.5 -11X + X2 = 0 + -24.5 Combine like terms: 0 + -24.5 = -24.5 -11X + X2 = -24.5 The X term is -11X. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11X + 30.25 + X2 = -24.5 + 30.25 Reorder the terms: 30.25 + -11X + X2 = -24.5 + 30.25 Combine like terms: -24.5 + 30.25 = 5.75 30.25 + -11X + X2 = 5.75 Factor a perfect square on the left side: (X + -5.5)(X + -5.5) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (X + -5.5) equal to 2.397915762 and -2.397915762.Subproblem 1
X + -5.5 = 2.397915762 Simplifying X + -5.5 = 2.397915762 Reorder the terms: -5.5 + X = 2.397915762 Solving -5.5 + X = 2.397915762 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + X = 2.397915762 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + X = 2.397915762 + 5.5 X = 2.397915762 + 5.5 Combine like terms: 2.397915762 + 5.5 = 7.897915762 X = 7.897915762 Simplifying X = 7.897915762Subproblem 2
X + -5.5 = -2.397915762 Simplifying X + -5.5 = -2.397915762 Reorder the terms: -5.5 + X = -2.397915762 Solving -5.5 + X = -2.397915762 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + X = -2.397915762 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + X = -2.397915762 + 5.5 X = -2.397915762 + 5.5 Combine like terms: -2.397915762 + 5.5 = 3.102084238 X = 3.102084238 Simplifying X = 3.102084238Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.897915762, 3.102084238}
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