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Simplifying (24x2) + -72x + 44 = 0 Reorder the terms: 44 + -72x + (24x2) = 0 Solving 44 + -72x + (24x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(11 + -18x + (6x2)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(11 + -18x + (6x2))' equal to zero and attempt to solve: Simplifying 11 + -18x + (6x2) = 0 Solving 11 + -18x + (6x2) = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.833333333 + -3x + x2 = 0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + -3x + -1.833333333 + x2 = 0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + -3x + x2 = 0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + -3x + x2 = 0 + -1.833333333 -3x + x2 = 0 + -1.833333333 Combine like terms: 0 + -1.833333333 = -1.833333333 -3x + x2 = -1.833333333 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.833333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.833333333 + 2.25 Combine like terms: -1.833333333 + 2.25 = 0.416666667 2.25 + -3x + x2 = 0.416666667 Factor a perfect square on the left side: ((x) + -1.5)((x) + -1.5) = 0.416666667 Calculate the square root of the right side: 0.645497225 Break this problem into two subproblems by setting ((x) + -1.5) equal to 0.645497225 and -0.645497225.Subproblem 1
(x) + -1.5 = 0.645497225 Simplifying (x) + -1.5 = 0.645497225 x + -1.5 = 0.645497225 Reorder the terms: -1.5 + x = 0.645497225 Solving -1.5 + x = 0.645497225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.645497225 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.645497225 + 1.5 x = 0.645497225 + 1.5 Combine like terms: 0.645497225 + 1.5 = 2.145497225 x = 2.145497225 Simplifying x = 2.145497225Subproblem 2
(x) + -1.5 = -0.645497225 Simplifying (x) + -1.5 = -0.645497225 x + -1.5 = -0.645497225 Reorder the terms: -1.5 + x = -0.645497225 Solving -1.5 + x = -0.645497225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.645497225 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.645497225 + 1.5 x = -0.645497225 + 1.5 Combine like terms: -0.645497225 + 1.5 = 0.854502775 x = 0.854502775 Simplifying x = 0.854502775Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.145497225, 0.854502775}Solution
x = {2.145497225, 0.854502775}
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