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Simplifying 8x2 + 18x + 8 = 0 Reorder the terms: 8 + 18x + 8x2 = 0 Solving 8 + 18x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 9x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 9x + 4x2)' equal to zero and attempt to solve: Simplifying 4 + 9x + 4x2 = 0 Solving 4 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + 2.25x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.25x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.25x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.25x + x2 = 0 + -1 2.25x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.25x + x2 = -1 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = -1 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = -1 + 1.265625 Combine like terms: -1 + 1.265625 = 0.265625 1.265625 + 2.25x + x2 = 0.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (x + 1.125) equal to 0.515388203 and -0.515388203.Subproblem 1
x + 1.125 = 0.515388203 Simplifying x + 1.125 = 0.515388203 Reorder the terms: 1.125 + x = 0.515388203 Solving 1.125 + x = 0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 0.515388203 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 0.515388203 + -1.125 x = 0.515388203 + -1.125 Combine like terms: 0.515388203 + -1.125 = -0.609611797 x = -0.609611797 Simplifying x = -0.609611797Subproblem 2
x + 1.125 = -0.515388203 Simplifying x + 1.125 = -0.515388203 Reorder the terms: 1.125 + x = -0.515388203 Solving 1.125 + x = -0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -0.515388203 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -0.515388203 + -1.125 x = -0.515388203 + -1.125 Combine like terms: -0.515388203 + -1.125 = -1.640388203 x = -1.640388203 Simplifying x = -1.640388203Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.609611797, -1.640388203}Solution
x = {-0.609611797, -1.640388203}
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