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Simplifying 2x2 + 84x + 40 = 0 Reorder the terms: 40 + 84x + 2x2 = 0 Solving 40 + 84x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + 42x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + 42x + x2)' equal to zero and attempt to solve: Simplifying 20 + 42x + x2 = 0 Solving 20 + 42x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 42x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 42x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 42x + x2 = 0 + -20 42x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 42x + x2 = -20 The x term is 42x. Take half its coefficient (21). Square it (441) and add it to both sides. Add '441' to each side of the equation. 42x + 441 + x2 = -20 + 441 Reorder the terms: 441 + 42x + x2 = -20 + 441 Combine like terms: -20 + 441 = 421 441 + 42x + x2 = 421 Factor a perfect square on the left side: (x + 21)(x + 21) = 421 Calculate the square root of the right side: 20.518284529 Break this problem into two subproblems by setting (x + 21) equal to 20.518284529 and -20.518284529.Subproblem 1
x + 21 = 20.518284529 Simplifying x + 21 = 20.518284529 Reorder the terms: 21 + x = 20.518284529 Solving 21 + x = 20.518284529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = 20.518284529 + -21 Combine like terms: 21 + -21 = 0 0 + x = 20.518284529 + -21 x = 20.518284529 + -21 Combine like terms: 20.518284529 + -21 = -0.481715471 x = -0.481715471 Simplifying x = -0.481715471Subproblem 2
x + 21 = -20.518284529 Simplifying x + 21 = -20.518284529 Reorder the terms: 21 + x = -20.518284529 Solving 21 + x = -20.518284529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = -20.518284529 + -21 Combine like terms: 21 + -21 = 0 0 + x = -20.518284529 + -21 x = -20.518284529 + -21 Combine like terms: -20.518284529 + -21 = -41.518284529 x = -41.518284529 Simplifying x = -41.518284529Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.481715471, -41.518284529}Solution
x = {-0.481715471, -41.518284529}
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