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Simplifying 6x2 + 160x + 64 = 0 Reorder the terms: 64 + 160x + 6x2 = 0 Solving 64 + 160x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(32 + 80x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + 80x + 3x2)' equal to zero and attempt to solve: Simplifying 32 + 80x + 3x2 = 0 Solving 32 + 80x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10.66666667 + 26.66666667x + x2 = 0 Move the constant term to the right: Add '-10.66666667' to each side of the equation. 10.66666667 + 26.66666667x + -10.66666667 + x2 = 0 + -10.66666667 Reorder the terms: 10.66666667 + -10.66666667 + 26.66666667x + x2 = 0 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + 26.66666667x + x2 = 0 + -10.66666667 26.66666667x + x2 = 0 + -10.66666667 Combine like terms: 0 + -10.66666667 = -10.66666667 26.66666667x + x2 = -10.66666667 The x term is 26.66666667x. Take half its coefficient (13.33333334). Square it (177.7777780) and add it to both sides. Add '177.7777780' to each side of the equation. 26.66666667x + 177.7777780 + x2 = -10.66666667 + 177.7777780 Reorder the terms: 177.7777780 + 26.66666667x + x2 = -10.66666667 + 177.7777780 Combine like terms: -10.66666667 + 177.7777780 = 167.11111133 177.7777780 + 26.66666667x + x2 = 167.11111133 Factor a perfect square on the left side: (x + 13.33333334)(x + 13.33333334) = 167.11111133 Calculate the square root of the right side: 12.927146295 Break this problem into two subproblems by setting (x + 13.33333334) equal to 12.927146295 and -12.927146295.Subproblem 1
x + 13.33333334 = 12.927146295 Simplifying x + 13.33333334 = 12.927146295 Reorder the terms: 13.33333334 + x = 12.927146295 Solving 13.33333334 + x = 12.927146295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.33333334' to each side of the equation. 13.33333334 + -13.33333334 + x = 12.927146295 + -13.33333334 Combine like terms: 13.33333334 + -13.33333334 = 0.00000000 0.00000000 + x = 12.927146295 + -13.33333334 x = 12.927146295 + -13.33333334 Combine like terms: 12.927146295 + -13.33333334 = -0.406187045 x = -0.406187045 Simplifying x = -0.406187045Subproblem 2
x + 13.33333334 = -12.927146295 Simplifying x + 13.33333334 = -12.927146295 Reorder the terms: 13.33333334 + x = -12.927146295 Solving 13.33333334 + x = -12.927146295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.33333334' to each side of the equation. 13.33333334 + -13.33333334 + x = -12.927146295 + -13.33333334 Combine like terms: 13.33333334 + -13.33333334 = 0.00000000 0.00000000 + x = -12.927146295 + -13.33333334 x = -12.927146295 + -13.33333334 Combine like terms: -12.927146295 + -13.33333334 = -26.260479635 x = -26.260479635 Simplifying x = -26.260479635Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.406187045, -26.260479635}Solution
x = {-0.406187045, -26.260479635}
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