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Simplifying 12x2 + 58x = 125 Reorder the terms: 58x + 12x2 = 125 Solving 58x + 12x2 = 125 Solving for variable 'x'. Reorder the terms: -125 + 58x + 12x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + 58x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -10.41666667 + 4.833333333x + x2 = 0 Move the constant term to the right: Add '10.41666667' to each side of the equation. -10.41666667 + 4.833333333x + 10.41666667 + x2 = 0 + 10.41666667 Reorder the terms: -10.41666667 + 10.41666667 + 4.833333333x + x2 = 0 + 10.41666667 Combine like terms: -10.41666667 + 10.41666667 = 0.00000000 0.00000000 + 4.833333333x + x2 = 0 + 10.41666667 4.833333333x + x2 = 0 + 10.41666667 Combine like terms: 0 + 10.41666667 = 10.41666667 4.833333333x + x2 = 10.41666667 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 = 10.41666667 + 5.840277779 Reorder the terms: 5.840277779 + 4.833333333x + x2 = 10.41666667 + 5.840277779 Combine like terms: 10.41666667 + 5.840277779 = 16.256944449 5.840277779 + 4.833333333x + x2 = 16.256944449 Factor a perfect square on the left side: (x + 2.416666667)(x + 2.416666667) = 16.256944449 Calculate the square root of the right side: 4.031990135 Break this problem into two subproblems by setting (x + 2.416666667) equal to 4.031990135 and -4.031990135.Subproblem 1
x + 2.416666667 = 4.031990135 Simplifying x + 2.416666667 = 4.031990135 Reorder the terms: 2.416666667 + x = 4.031990135 Solving 2.416666667 + x = 4.031990135 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 = 4.031990135 + -2.416666667 Combine like terms: 2.416666667 + -2.416666667 = 0.000000000 0.000000000 + x = 4.031990135 + -2.416666667 x = 4.031990135 + -2.416666667 Combine like terms: 4.031990135 + -2.416666667 = 1.615323468 x = 1.615323468 Simplifying x = 1.615323468Subproblem 2
x + 2.416666667 = -4.031990135 Simplifying x + 2.416666667 = -4.031990135 Reorder the terms: 2.416666667 + x = -4.031990135 Solving 2.416666667 + x = -4.031990135 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 = -4.031990135 + -2.416666667 Combine like terms: 2.416666667 + -2.416666667 = 0.000000000 0.000000000 + x = -4.031990135 + -2.416666667 x = -4.031990135 + -2.416666667 Combine like terms: -4.031990135 + -2.416666667 = -6.448656802 x = -6.448656802 Simplifying x = -6.448656802Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.615323468, -6.448656802}
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