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Simplifying 2x2 + -28x + 20 = 0 Reorder the terms: 20 + -28x + 2x2 = 0 Solving 20 + -28x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + -14x + x2)' equal to zero and attempt to solve: Simplifying 10 + -14x + x2 = 0 Solving 10 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -14x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -14x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -14x + x2 = 0 + -10 -14x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -14x + x2 = -10 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -10 + 49 Reorder the terms: 49 + -14x + x2 = -10 + 49 Combine like terms: -10 + 49 = 39 49 + -14x + x2 = 39 Factor a perfect square on the left side: (x + -7)(x + -7) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + -7) equal to 6.244997998 and -6.244997998.Subproblem 1
x + -7 = 6.244997998 Simplifying x + -7 = 6.244997998 Reorder the terms: -7 + x = 6.244997998 Solving -7 + x = 6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 6.244997998 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.244997998 + 7 x = 6.244997998 + 7 Combine like terms: 6.244997998 + 7 = 13.244997998 x = 13.244997998 Simplifying x = 13.244997998Subproblem 2
x + -7 = -6.244997998 Simplifying x + -7 = -6.244997998 Reorder the terms: -7 + x = -6.244997998 Solving -7 + x = -6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -6.244997998 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.244997998 + 7 x = -6.244997998 + 7 Combine like terms: -6.244997998 + 7 = 0.755002002 x = 0.755002002 Simplifying x = 0.755002002Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.244997998, 0.755002002}Solution
x = {13.244997998, 0.755002002}
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