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Simplifying 15x2 + -82x + 24 = 0 Reorder the terms: 24 + -82x + 15x2 = 0 Solving 24 + -82x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.6 + -5.466666667x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -5.466666667x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -5.466666667x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -5.466666667x + x2 = 0 + -1.6 -5.466666667x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -5.466666667x + x2 = -1.6 The x term is -5.466666667x. Take half its coefficient (-2.733333334). Square it (7.471111115) and add it to both sides. Add '7.471111115' to each side of the equation. -5.466666667x + 7.471111115 + x2 = -1.6 + 7.471111115 Reorder the terms: 7.471111115 + -5.466666667x + x2 = -1.6 + 7.471111115 Combine like terms: -1.6 + 7.471111115 = 5.871111115 7.471111115 + -5.466666667x + x2 = 5.871111115 Factor a perfect square on the left side: (x + -2.733333334)(x + -2.733333334) = 5.871111115 Calculate the square root of the right side: 2.42303758 Break this problem into two subproblems by setting (x + -2.733333334) equal to 2.42303758 and -2.42303758.Subproblem 1
x + -2.733333334 = 2.42303758 Simplifying x + -2.733333334 = 2.42303758 Reorder the terms: -2.733333334 + x = 2.42303758 Solving -2.733333334 + x = 2.42303758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.733333334' to each side of the equation. -2.733333334 + 2.733333334 + x = 2.42303758 + 2.733333334 Combine like terms: -2.733333334 + 2.733333334 = 0.000000000 0.000000000 + x = 2.42303758 + 2.733333334 x = 2.42303758 + 2.733333334 Combine like terms: 2.42303758 + 2.733333334 = 5.156370914 x = 5.156370914 Simplifying x = 5.156370914Subproblem 2
x + -2.733333334 = -2.42303758 Simplifying x + -2.733333334 = -2.42303758 Reorder the terms: -2.733333334 + x = -2.42303758 Solving -2.733333334 + x = -2.42303758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.733333334' to each side of the equation. -2.733333334 + 2.733333334 + x = -2.42303758 + 2.733333334 Combine like terms: -2.733333334 + 2.733333334 = 0.000000000 0.000000000 + x = -2.42303758 + 2.733333334 x = -2.42303758 + 2.733333334 Combine like terms: -2.42303758 + 2.733333334 = 0.310295754 x = 0.310295754 Simplifying x = 0.310295754Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.156370914, 0.310295754}
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