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Simplifying 36x2 + -176x + -304 = 0 Reorder the terms: -304 + -176x + 36x2 = 0 Solving -304 + -176x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-76 + -44x + 9x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-76 + -44x + 9x2)' equal to zero and attempt to solve: Simplifying -76 + -44x + 9x2 = 0 Solving -76 + -44x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -8.444444444 + -4.888888889x + x2 = 0 Move the constant term to the right: Add '8.444444444' to each side of the equation. -8.444444444 + -4.888888889x + 8.444444444 + x2 = 0 + 8.444444444 Reorder the terms: -8.444444444 + 8.444444444 + -4.888888889x + x2 = 0 + 8.444444444 Combine like terms: -8.444444444 + 8.444444444 = 0.000000000 0.000000000 + -4.888888889x + x2 = 0 + 8.444444444 -4.888888889x + x2 = 0 + 8.444444444 Combine like terms: 0 + 8.444444444 = 8.444444444 -4.888888889x + x2 = 8.444444444 The x term is -4.888888889x. Take half its coefficient (-2.444444445). Square it (5.975308645) and add it to both sides. Add '5.975308645' to each side of the equation. -4.888888889x + 5.975308645 + x2 = 8.444444444 + 5.975308645 Reorder the terms: 5.975308645 + -4.888888889x + x2 = 8.444444444 + 5.975308645 Combine like terms: 8.444444444 + 5.975308645 = 14.419753089 5.975308645 + -4.888888889x + x2 = 14.419753089 Factor a perfect square on the left side: (x + -2.444444445)(x + -2.444444445) = 14.419753089 Calculate the square root of the right side: 3.797334998 Break this problem into two subproblems by setting (x + -2.444444445) equal to 3.797334998 and -3.797334998.Subproblem 1
x + -2.444444445 = 3.797334998 Simplifying x + -2.444444445 = 3.797334998 Reorder the terms: -2.444444445 + x = 3.797334998 Solving -2.444444445 + x = 3.797334998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.444444445' to each side of the equation. -2.444444445 + 2.444444445 + x = 3.797334998 + 2.444444445 Combine like terms: -2.444444445 + 2.444444445 = 0.000000000 0.000000000 + x = 3.797334998 + 2.444444445 x = 3.797334998 + 2.444444445 Combine like terms: 3.797334998 + 2.444444445 = 6.241779443 x = 6.241779443 Simplifying x = 6.241779443Subproblem 2
x + -2.444444445 = -3.797334998 Simplifying x + -2.444444445 = -3.797334998 Reorder the terms: -2.444444445 + x = -3.797334998 Solving -2.444444445 + x = -3.797334998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.444444445' to each side of the equation. -2.444444445 + 2.444444445 + x = -3.797334998 + 2.444444445 Combine like terms: -2.444444445 + 2.444444445 = 0.000000000 0.000000000 + x = -3.797334998 + 2.444444445 x = -3.797334998 + 2.444444445 Combine like terms: -3.797334998 + 2.444444445 = -1.352890553 x = -1.352890553 Simplifying x = -1.352890553Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.241779443, -1.352890553}Solution
x = {6.241779443, -1.352890553}
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