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Simplifying 12x2 + 58x + -280 = 0 Reorder the terms: -280 + 58x + 12x2 = 0 Solving -280 + 58x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-140 + 29x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-140 + 29x + 6x2)' equal to zero and attempt to solve: Simplifying -140 + 29x + 6x2 = 0 Solving -140 + 29x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -23.33333333 + 4.833333333x + x2 = 0 Move the constant term to the right: Add '23.33333333' to each side of the equation. -23.33333333 + 4.833333333x + 23.33333333 + x2 = 0 + 23.33333333 Reorder the terms: -23.33333333 + 23.33333333 + 4.833333333x + x2 = 0 + 23.33333333 Combine like terms: -23.33333333 + 23.33333333 = 0.00000000 0.00000000 + 4.833333333x + x2 = 0 + 23.33333333 4.833333333x + x2 = 0 + 23.33333333 Combine like terms: 0 + 23.33333333 = 23.33333333 4.833333333x + x2 = 23.33333333 The x term is 4.833333333x. Take half its coefficient (2.416666667). Square it (5.840277779) and add it to both sides. Add '5.840277779' to each side of the equation. 4.833333333x + 5.840277779 + x2 = 23.33333333 + 5.840277779 Reorder the terms: 5.840277779 + 4.833333333x + x2 = 23.33333333 + 5.840277779 Combine like terms: 23.33333333 + 5.840277779 = 29.173611109 5.840277779 + 4.833333333x + x2 = 29.173611109 Factor a perfect square on the left side: (x + 2.416666667)(x + 2.416666667) = 29.173611109 Calculate the square root of the right side: 5.401260141 Break this problem into two subproblems by setting (x + 2.416666667) equal to 5.401260141 and -5.401260141.Subproblem 1
x + 2.416666667 = 5.401260141 Simplifying x + 2.416666667 = 5.401260141 Reorder the terms: 2.416666667 + x = 5.401260141 Solving 2.416666667 + x = 5.401260141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.416666667' to each side of the equation. 2.416666667 + -2.416666667 + x = 5.401260141 + -2.416666667 Combine like terms: 2.416666667 + -2.416666667 = 0.000000000 0.000000000 + x = 5.401260141 + -2.416666667 x = 5.401260141 + -2.416666667 Combine like terms: 5.401260141 + -2.416666667 = 2.984593474 x = 2.984593474 Simplifying x = 2.984593474Subproblem 2
x + 2.416666667 = -5.401260141 Simplifying x + 2.416666667 = -5.401260141 Reorder the terms: 2.416666667 + x = -5.401260141 Solving 2.416666667 + x = -5.401260141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.416666667' to each side of the equation. 2.416666667 + -2.416666667 + x = -5.401260141 + -2.416666667 Combine like terms: 2.416666667 + -2.416666667 = 0.000000000 0.000000000 + x = -5.401260141 + -2.416666667 x = -5.401260141 + -2.416666667 Combine like terms: -5.401260141 + -2.416666667 = -7.817926808 x = -7.817926808 Simplifying x = -7.817926808Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.984593474, -7.817926808}Solution
x = {2.984593474, -7.817926808}
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