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Simplifying 72x2 + 80x + 20 = 0 Reorder the terms: 20 + 80x + 72x2 = 0 Solving 20 + 80x + 72x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 20x + 18x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 20x + 18x2)' equal to zero and attempt to solve: Simplifying 5 + 20x + 18x2 = 0 Solving 5 + 20x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.2777777778 + 1.111111111x + x2 = 0 Move the constant term to the right: Add '-0.2777777778' to each side of the equation. 0.2777777778 + 1.111111111x + -0.2777777778 + x2 = 0 + -0.2777777778 Reorder the terms: 0.2777777778 + -0.2777777778 + 1.111111111x + x2 = 0 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + 1.111111111x + x2 = 0 + -0.2777777778 1.111111111x + x2 = 0 + -0.2777777778 Combine like terms: 0 + -0.2777777778 = -0.2777777778 1.111111111x + x2 = -0.2777777778 The x term is 1.111111111x. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111x + 0.3086419752 + x2 = -0.2777777778 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111x + x2 = -0.2777777778 + 0.3086419752 Combine like terms: -0.2777777778 + 0.3086419752 = 0.0308641974 0.3086419752 + 1.111111111x + x2 = 0.0308641974 Factor a perfect square on the left side: (x + 0.5555555555)(x + 0.5555555555) = 0.0308641974 Calculate the square root of the right side: 0.175682092 Break this problem into two subproblems by setting (x + 0.5555555555) equal to 0.175682092 and -0.175682092.Subproblem 1
x + 0.5555555555 = 0.175682092 Simplifying x + 0.5555555555 = 0.175682092 Reorder the terms: 0.5555555555 + x = 0.175682092 Solving 0.5555555555 + x = 0.175682092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = 0.175682092 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 0.175682092 + -0.5555555555 x = 0.175682092 + -0.5555555555 Combine like terms: 0.175682092 + -0.5555555555 = -0.3798734635 x = -0.3798734635 Simplifying x = -0.3798734635Subproblem 2
x + 0.5555555555 = -0.175682092 Simplifying x + 0.5555555555 = -0.175682092 Reorder the terms: 0.5555555555 + x = -0.175682092 Solving 0.5555555555 + x = -0.175682092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = -0.175682092 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -0.175682092 + -0.5555555555 x = -0.175682092 + -0.5555555555 Combine like terms: -0.175682092 + -0.5555555555 = -0.7312376475 x = -0.7312376475 Simplifying x = -0.7312376475Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.3798734635, -0.7312376475}Solution
x = {-0.3798734635, -0.7312376475}
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