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Simplifying 24x2 + -44x + 7 = 0 Reorder the terms: 7 + -44x + 24x2 = 0 Solving 7 + -44x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.2916666667 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '-0.2916666667' to each side of the equation. 0.2916666667 + -1.833333333x + -0.2916666667 + x2 = 0 + -0.2916666667 Reorder the terms: 0.2916666667 + -0.2916666667 + -1.833333333x + x2 = 0 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + -1.833333333x + x2 = 0 + -0.2916666667 -1.833333333x + x2 = 0 + -0.2916666667 Combine like terms: 0 + -0.2916666667 = -0.2916666667 -1.833333333x + x2 = -0.2916666667 The x term is -1.833333333x. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333x + 0.8402777775 + x2 = -0.2916666667 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = -0.2916666667 + 0.8402777775 Combine like terms: -0.2916666667 + 0.8402777775 = 0.5486111108 0.8402777775 + -1.833333333x + x2 = 0.5486111108 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 0.5486111108 Calculate the square root of the right side: 0.740682868 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 0.740682868 and -0.740682868.Subproblem 1
x + -0.9166666665 = 0.740682868 Simplifying x + -0.9166666665 = 0.740682868 Reorder the terms: -0.9166666665 + x = 0.740682868 Solving -0.9166666665 + x = 0.740682868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = 0.740682868 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 0.740682868 + 0.9166666665 x = 0.740682868 + 0.9166666665 Combine like terms: 0.740682868 + 0.9166666665 = 1.6573495345 x = 1.6573495345 Simplifying x = 1.6573495345Subproblem 2
x + -0.9166666665 = -0.740682868 Simplifying x + -0.9166666665 = -0.740682868 Reorder the terms: -0.9166666665 + x = -0.740682868 Solving -0.9166666665 + x = -0.740682868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = -0.740682868 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -0.740682868 + 0.9166666665 x = -0.740682868 + 0.9166666665 Combine like terms: -0.740682868 + 0.9166666665 = 0.1759837985 x = 0.1759837985 Simplifying x = 0.1759837985Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6573495345, 0.1759837985}
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