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Simplifying 2x2 + -42x + 104 = 0 Reorder the terms: 104 + -42x + 2x2 = 0 Solving 104 + -42x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(52 + -21x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(52 + -21x + x2)' equal to zero and attempt to solve: Simplifying 52 + -21x + x2 = 0 Solving 52 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + -21x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + -21x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -21x + x2 = 0 + -52 -21x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 -21x + x2 = -52 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -52 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -52 + 110.25 Combine like terms: -52 + 110.25 = 58.25 110.25 + -21x + x2 = 58.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + -10.5) equal to 7.632168761 and -7.632168761.Subproblem 1
x + -10.5 = 7.632168761 Simplifying x + -10.5 = 7.632168761 Reorder the terms: -10.5 + x = 7.632168761 Solving -10.5 + x = 7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 7.632168761 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 7.632168761 + 10.5 x = 7.632168761 + 10.5 Combine like terms: 7.632168761 + 10.5 = 18.132168761 x = 18.132168761 Simplifying x = 18.132168761Subproblem 2
x + -10.5 = -7.632168761 Simplifying x + -10.5 = -7.632168761 Reorder the terms: -10.5 + x = -7.632168761 Solving -10.5 + x = -7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -7.632168761 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -7.632168761 + 10.5 x = -7.632168761 + 10.5 Combine like terms: -7.632168761 + 10.5 = 2.867831239 x = 2.867831239 Simplifying x = 2.867831239Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.132168761, 2.867831239}Solution
x = {18.132168761, 2.867831239}
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