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Simplifying 2x2 + 20x + 100 = 196 Reorder the terms: 100 + 20x + 2x2 = 196 Solving 100 + 20x + 2x2 = 196 Solving for variable 'x'. Reorder the terms: 100 + -196 + 20x + 2x2 = 196 + -196 Combine like terms: 100 + -196 = -96 -96 + 20x + 2x2 = 196 + -196 Combine like terms: 196 + -196 = 0 -96 + 20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-48 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-48 + 10x + x2)' equal to zero and attempt to solve: Simplifying -48 + 10x + x2 = 0 Solving -48 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 10x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 10x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 10x + x2 = 0 + 48 10x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 10x + x2 = 48 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 = 48 + 25 Reorder the terms: 25 + 10x + x2 = 48 + 25 Combine like terms: 48 + 25 = 73 25 + 10x + x2 = 73 Factor a perfect square on the left side: (x + 5)(x + 5) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 5) equal to 8.544003745 and -8.544003745.Subproblem 1
x + 5 = 8.544003745 Simplifying x + 5 = 8.544003745 Reorder the terms: 5 + x = 8.544003745 Solving 5 + x = 8.544003745 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 = 8.544003745 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.544003745 + -5 x = 8.544003745 + -5 Combine like terms: 8.544003745 + -5 = 3.544003745 x = 3.544003745 Simplifying x = 3.544003745Subproblem 2
x + 5 = -8.544003745 Simplifying x + 5 = -8.544003745 Reorder the terms: 5 + x = -8.544003745 Solving 5 + x = -8.544003745 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 = -8.544003745 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.544003745 + -5 x = -8.544003745 + -5 Combine like terms: -8.544003745 + -5 = -13.544003745 x = -13.544003745 Simplifying x = -13.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.544003745, -13.544003745}Solution
x = {3.544003745, -13.544003745}
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