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Simplifying 36x2 + 134x + 8 = 0 Reorder the terms: 8 + 134x + 36x2 = 0 Solving 8 + 134x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 67x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 67x + 18x2)' equal to zero and attempt to solve: Simplifying 4 + 67x + 18x2 = 0 Solving 4 + 67x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.2222222222 + 3.722222222x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 3.722222222x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 3.722222222x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 3.722222222x + x2 = 0 + -0.2222222222 3.722222222x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 3.722222222x + x2 = -0.2222222222 The x term is 3.722222222x. Take half its coefficient (1.861111111). Square it (3.463734567) and add it to both sides. Add '3.463734567' to each side of the equation. 3.722222222x + 3.463734567 + x2 = -0.2222222222 + 3.463734567 Reorder the terms: 3.463734567 + 3.722222222x + x2 = -0.2222222222 + 3.463734567 Combine like terms: -0.2222222222 + 3.463734567 = 3.2415123448 3.463734567 + 3.722222222x + x2 = 3.2415123448 Factor a perfect square on the left side: (x + 1.861111111)(x + 1.861111111) = 3.2415123448 Calculate the square root of the right side: 1.800420047 Break this problem into two subproblems by setting (x + 1.861111111) equal to 1.800420047 and -1.800420047.Subproblem 1
x + 1.861111111 = 1.800420047 Simplifying x + 1.861111111 = 1.800420047 Reorder the terms: 1.861111111 + x = 1.800420047 Solving 1.861111111 + x = 1.800420047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.861111111' to each side of the equation. 1.861111111 + -1.861111111 + x = 1.800420047 + -1.861111111 Combine like terms: 1.861111111 + -1.861111111 = 0.000000000 0.000000000 + x = 1.800420047 + -1.861111111 x = 1.800420047 + -1.861111111 Combine like terms: 1.800420047 + -1.861111111 = -0.060691064 x = -0.060691064 Simplifying x = -0.060691064Subproblem 2
x + 1.861111111 = -1.800420047 Simplifying x + 1.861111111 = -1.800420047 Reorder the terms: 1.861111111 + x = -1.800420047 Solving 1.861111111 + x = -1.800420047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.861111111' to each side of the equation. 1.861111111 + -1.861111111 + x = -1.800420047 + -1.861111111 Combine like terms: 1.861111111 + -1.861111111 = 0.000000000 0.000000000 + x = -1.800420047 + -1.861111111 x = -1.800420047 + -1.861111111 Combine like terms: -1.800420047 + -1.861111111 = -3.661531158 x = -3.661531158 Simplifying x = -3.661531158Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.060691064, -3.661531158}Solution
x = {-0.060691064, -3.661531158}
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