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Simplifying 0.49x2 + 12x = 20 Reorder the terms: 12x + 0.49x2 = 20 Solving 12x + 0.49x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 12x + 0.49x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 12x + 0.49x2 = 0 Begin completing the square. Divide all terms by 0.49 the coefficient of the squared term: Divide each side by '0.49'. -40.81632653 + 24.48979592x + x2 = 0 Move the constant term to the right: Add '40.81632653' to each side of the equation. -40.81632653 + 24.48979592x + 40.81632653 + x2 = 0 + 40.81632653 Reorder the terms: -40.81632653 + 40.81632653 + 24.48979592x + x2 = 0 + 40.81632653 Combine like terms: -40.81632653 + 40.81632653 = 0.00000000 0.00000000 + 24.48979592x + x2 = 0 + 40.81632653 24.48979592x + x2 = 0 + 40.81632653 Combine like terms: 0 + 40.81632653 = 40.81632653 24.48979592x + x2 = 40.81632653 The x term is 24.48979592x. Take half its coefficient (12.24489796). Square it (149.9375261) and add it to both sides. Add '149.9375261' to each side of the equation. 24.48979592x + 149.9375261 + x2 = 40.81632653 + 149.9375261 Reorder the terms: 149.9375261 + 24.48979592x + x2 = 40.81632653 + 149.9375261 Combine like terms: 40.81632653 + 149.9375261 = 190.75385263 149.9375261 + 24.48979592x + x2 = 190.75385263 Factor a perfect square on the left side: (x + 12.24489796)(x + 12.24489796) = 190.75385263 Calculate the square root of the right side: 13.811366791 Break this problem into two subproblems by setting (x + 12.24489796) equal to 13.811366791 and -13.811366791.Subproblem 1
x + 12.24489796 = 13.811366791 Simplifying x + 12.24489796 = 13.811366791 Reorder the terms: 12.24489796 + x = 13.811366791 Solving 12.24489796 + x = 13.811366791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.24489796' to each side of the equation. 12.24489796 + -12.24489796 + x = 13.811366791 + -12.24489796 Combine like terms: 12.24489796 + -12.24489796 = 0.00000000 0.00000000 + x = 13.811366791 + -12.24489796 x = 13.811366791 + -12.24489796 Combine like terms: 13.811366791 + -12.24489796 = 1.566468831 x = 1.566468831 Simplifying x = 1.566468831Subproblem 2
x + 12.24489796 = -13.811366791 Simplifying x + 12.24489796 = -13.811366791 Reorder the terms: 12.24489796 + x = -13.811366791 Solving 12.24489796 + x = -13.811366791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.24489796' to each side of the equation. 12.24489796 + -12.24489796 + x = -13.811366791 + -12.24489796 Combine like terms: 12.24489796 + -12.24489796 = 0.00000000 0.00000000 + x = -13.811366791 + -12.24489796 x = -13.811366791 + -12.24489796 Combine like terms: -13.811366791 + -12.24489796 = -26.056264751 x = -26.056264751 Simplifying x = -26.056264751Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.566468831, -26.056264751}
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