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Simplifying 24x2 + -86x + 30 = 0 Reorder the terms: 30 + -86x + 24x2 = 0 Solving 30 + -86x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -43x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -43x + 12x2)' equal to zero and attempt to solve: Simplifying 15 + -43x + 12x2 = 0 Solving 15 + -43x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 1.25 + -3.583333333x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -3.583333333x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -3.583333333x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -3.583333333x + x2 = 0 + -1.25 -3.583333333x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -3.583333333x + x2 = -1.25 The x term is -3.583333333x. Take half its coefficient (-1.791666667). Square it (3.210069446) and add it to both sides. Add '3.210069446' to each side of the equation. -3.583333333x + 3.210069446 + x2 = -1.25 + 3.210069446 Reorder the terms: 3.210069446 + -3.583333333x + x2 = -1.25 + 3.210069446 Combine like terms: -1.25 + 3.210069446 = 1.960069446 3.210069446 + -3.583333333x + x2 = 1.960069446 Factor a perfect square on the left side: (x + -1.791666667)(x + -1.791666667) = 1.960069446 Calculate the square root of the right side: 1.400024802 Break this problem into two subproblems by setting (x + -1.791666667) equal to 1.400024802 and -1.400024802.Subproblem 1
x + -1.791666667 = 1.400024802 Simplifying x + -1.791666667 = 1.400024802 Reorder the terms: -1.791666667 + x = 1.400024802 Solving -1.791666667 + x = 1.400024802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.791666667' to each side of the equation. -1.791666667 + 1.791666667 + x = 1.400024802 + 1.791666667 Combine like terms: -1.791666667 + 1.791666667 = 0.000000000 0.000000000 + x = 1.400024802 + 1.791666667 x = 1.400024802 + 1.791666667 Combine like terms: 1.400024802 + 1.791666667 = 3.191691469 x = 3.191691469 Simplifying x = 3.191691469Subproblem 2
x + -1.791666667 = -1.400024802 Simplifying x + -1.791666667 = -1.400024802 Reorder the terms: -1.791666667 + x = -1.400024802 Solving -1.791666667 + x = -1.400024802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.791666667' to each side of the equation. -1.791666667 + 1.791666667 + x = -1.400024802 + 1.791666667 Combine like terms: -1.791666667 + 1.791666667 = 0.000000000 0.000000000 + x = -1.400024802 + 1.791666667 x = -1.400024802 + 1.791666667 Combine like terms: -1.400024802 + 1.791666667 = 0.391641865 x = 0.391641865 Simplifying x = 0.391641865Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.191691469, 0.391641865}Solution
x = {3.191691469, 0.391641865}
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