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Simplifying 21x2 + 192x + 180 = 0 Reorder the terms: 180 + 192x + 21x2 = 0 Solving 180 + 192x + 21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(60 + 64x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(60 + 64x + 7x2)' equal to zero and attempt to solve: Simplifying 60 + 64x + 7x2 = 0 Solving 60 + 64x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 8.571428571 + 9.142857143x + x2 = 0 Move the constant term to the right: Add '-8.571428571' to each side of the equation. 8.571428571 + 9.142857143x + -8.571428571 + x2 = 0 + -8.571428571 Reorder the terms: 8.571428571 + -8.571428571 + 9.142857143x + x2 = 0 + -8.571428571 Combine like terms: 8.571428571 + -8.571428571 = 0.000000000 0.000000000 + 9.142857143x + x2 = 0 + -8.571428571 9.142857143x + x2 = 0 + -8.571428571 Combine like terms: 0 + -8.571428571 = -8.571428571 9.142857143x + x2 = -8.571428571 The x term is 9.142857143x. Take half its coefficient (4.571428572). Square it (20.89795919) and add it to both sides. Add '20.89795919' to each side of the equation. 9.142857143x + 20.89795919 + x2 = -8.571428571 + 20.89795919 Reorder the terms: 20.89795919 + 9.142857143x + x2 = -8.571428571 + 20.89795919 Combine like terms: -8.571428571 + 20.89795919 = 12.326530619 20.89795919 + 9.142857143x + x2 = 12.326530619 Factor a perfect square on the left side: (x + 4.571428572)(x + 4.571428572) = 12.326530619 Calculate the square root of the right side: 3.510915923 Break this problem into two subproblems by setting (x + 4.571428572) equal to 3.510915923 and -3.510915923.Subproblem 1
x + 4.571428572 = 3.510915923 Simplifying x + 4.571428572 = 3.510915923 Reorder the terms: 4.571428572 + x = 3.510915923 Solving 4.571428572 + x = 3.510915923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.571428572' to each side of the equation. 4.571428572 + -4.571428572 + x = 3.510915923 + -4.571428572 Combine like terms: 4.571428572 + -4.571428572 = 0.000000000 0.000000000 + x = 3.510915923 + -4.571428572 x = 3.510915923 + -4.571428572 Combine like terms: 3.510915923 + -4.571428572 = -1.060512649 x = -1.060512649 Simplifying x = -1.060512649Subproblem 2
x + 4.571428572 = -3.510915923 Simplifying x + 4.571428572 = -3.510915923 Reorder the terms: 4.571428572 + x = -3.510915923 Solving 4.571428572 + x = -3.510915923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.571428572' to each side of the equation. 4.571428572 + -4.571428572 + x = -3.510915923 + -4.571428572 Combine like terms: 4.571428572 + -4.571428572 = 0.000000000 0.000000000 + x = -3.510915923 + -4.571428572 x = -3.510915923 + -4.571428572 Combine like terms: -3.510915923 + -4.571428572 = -8.082344495 x = -8.082344495 Simplifying x = -8.082344495Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.060512649, -8.082344495}Solution
x = {-1.060512649, -8.082344495}
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