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Simplifying 8x2 + 36x + 4 = 0 Reorder the terms: 4 + 36x + 8x2 = 0 Solving 4 + 36x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 9x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + 9x + 2x2 = 0 Solving 1 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 4.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 4.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 4.5x + x2 = 0 + -0.5 4.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 4.5x + x2 = -0.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = -0.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -0.5 + 5.0625 Combine like terms: -0.5 + 5.0625 = 4.5625 5.0625 + 4.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + 2.25) equal to 2.136000936 and -2.136000936.Subproblem 1
x + 2.25 = 2.136000936 Simplifying x + 2.25 = 2.136000936 Reorder the terms: 2.25 + x = 2.136000936 Solving 2.25 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.136000936 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.136000936 + -2.25 x = 2.136000936 + -2.25 Combine like terms: 2.136000936 + -2.25 = -0.113999064 x = -0.113999064 Simplifying x = -0.113999064Subproblem 2
x + 2.25 = -2.136000936 Simplifying x + 2.25 = -2.136000936 Reorder the terms: 2.25 + x = -2.136000936 Solving 2.25 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.136000936 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.136000936 + -2.25 x = -2.136000936 + -2.25 Combine like terms: -2.136000936 + -2.25 = -4.386000936 x = -4.386000936 Simplifying x = -4.386000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.113999064, -4.386000936}Solution
x = {-0.113999064, -4.386000936}
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