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Simplifying 8x2 + 36x + 8 = 0 Reorder the terms: 8 + 36x + 8x2 = 0 Solving 8 + 36x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + 9x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying 2 + 9x + 2x2 = 0 Solving 2 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 4.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 4.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4.5x + x2 = 0 + -1 4.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 4.5x + x2 = -1 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 = -1 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -1 + 5.0625 Combine like terms: -1 + 5.0625 = 4.0625 5.0625 + 4.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + 2.25) equal to 2.015564437 and -2.015564437.Subproblem 1
x + 2.25 = 2.015564437 Simplifying x + 2.25 = 2.015564437 Reorder the terms: 2.25 + x = 2.015564437 Solving 2.25 + x = 2.015564437 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 = 2.015564437 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.015564437 + -2.25 x = 2.015564437 + -2.25 Combine like terms: 2.015564437 + -2.25 = -0.234435563 x = -0.234435563 Simplifying x = -0.234435563Subproblem 2
x + 2.25 = -2.015564437 Simplifying x + 2.25 = -2.015564437 Reorder the terms: 2.25 + x = -2.015564437 Solving 2.25 + x = -2.015564437 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 = -2.015564437 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.015564437 + -2.25 x = -2.015564437 + -2.25 Combine like terms: -2.015564437 + -2.25 = -4.265564437 x = -4.265564437 Simplifying x = -4.265564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.234435563, -4.265564437}Solution
x = {-0.234435563, -4.265564437}
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