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Simplifying 36x2 + -276x + 160 = 0 Reorder the terms: 160 + -276x + 36x2 = 0 Solving 160 + -276x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(40 + -69x + 9x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(40 + -69x + 9x2)' equal to zero and attempt to solve: Simplifying 40 + -69x + 9x2 = 0 Solving 40 + -69x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 4.444444444 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '-4.444444444' to each side of the equation. 4.444444444 + -7.666666667x + -4.444444444 + x2 = 0 + -4.444444444 Reorder the terms: 4.444444444 + -4.444444444 + -7.666666667x + x2 = 0 + -4.444444444 Combine like terms: 4.444444444 + -4.444444444 = 0.000000000 0.000000000 + -7.666666667x + x2 = 0 + -4.444444444 -7.666666667x + x2 = 0 + -4.444444444 Combine like terms: 0 + -4.444444444 = -4.444444444 -7.666666667x + x2 = -4.444444444 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = -4.444444444 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = -4.444444444 + 14.69444445 Combine like terms: -4.444444444 + 14.69444445 = 10.250000006 14.69444445 + -7.666666667x + x2 = 10.250000006 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 10.250000006 Calculate the square root of the right side: 3.20156212 Break this problem into two subproblems by setting (x + -3.833333334) equal to 3.20156212 and -3.20156212.Subproblem 1
x + -3.833333334 = 3.20156212 Simplifying x + -3.833333334 = 3.20156212 Reorder the terms: -3.833333334 + x = 3.20156212 Solving -3.833333334 + x = 3.20156212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 3.20156212 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 3.20156212 + 3.833333334 x = 3.20156212 + 3.833333334 Combine like terms: 3.20156212 + 3.833333334 = 7.034895454 x = 7.034895454 Simplifying x = 7.034895454Subproblem 2
x + -3.833333334 = -3.20156212 Simplifying x + -3.833333334 = -3.20156212 Reorder the terms: -3.833333334 + x = -3.20156212 Solving -3.833333334 + x = -3.20156212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -3.20156212 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -3.20156212 + 3.833333334 x = -3.20156212 + 3.833333334 Combine like terms: -3.20156212 + 3.833333334 = 0.631771214 x = 0.631771214 Simplifying x = 0.631771214Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.034895454, 0.631771214}Solution
x = {7.034895454, 0.631771214}
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