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Simplifying -4.9x2 + 6.02x + 20 = 0 Reorder the terms: 20 + 6.02x + -4.9x2 = 0 Solving 20 + 6.02x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -4.081632653 + -1.228571429x + x2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + -1.228571429x + 4.081632653 + x2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + -1.228571429x + x2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + -1.228571429x + x2 = 0 + 4.081632653 -1.228571429x + x2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 -1.228571429x + x2 = 4.081632653 The x term is -1.228571429x. Take half its coefficient (-0.6142857145). Square it (0.3773469390) and add it to both sides. Add '0.3773469390' to each side of the equation. -1.228571429x + 0.3773469390 + x2 = 4.081632653 + 0.3773469390 Reorder the terms: 0.3773469390 + -1.228571429x + x2 = 4.081632653 + 0.3773469390 Combine like terms: 4.081632653 + 0.3773469390 = 4.458979592 0.3773469390 + -1.228571429x + x2 = 4.458979592 Factor a perfect square on the left side: (x + -0.6142857145)(x + -0.6142857145) = 4.458979592 Calculate the square root of the right side: 2.111629606 Break this problem into two subproblems by setting (x + -0.6142857145) equal to 2.111629606 and -2.111629606.Subproblem 1
x + -0.6142857145 = 2.111629606 Simplifying x + -0.6142857145 = 2.111629606 Reorder the terms: -0.6142857145 + x = 2.111629606 Solving -0.6142857145 + x = 2.111629606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6142857145' to each side of the equation. -0.6142857145 + 0.6142857145 + x = 2.111629606 + 0.6142857145 Combine like terms: -0.6142857145 + 0.6142857145 = 0.0000000000 0.0000000000 + x = 2.111629606 + 0.6142857145 x = 2.111629606 + 0.6142857145 Combine like terms: 2.111629606 + 0.6142857145 = 2.7259153205 x = 2.7259153205 Simplifying x = 2.7259153205Subproblem 2
x + -0.6142857145 = -2.111629606 Simplifying x + -0.6142857145 = -2.111629606 Reorder the terms: -0.6142857145 + x = -2.111629606 Solving -0.6142857145 + x = -2.111629606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6142857145' to each side of the equation. -0.6142857145 + 0.6142857145 + x = -2.111629606 + 0.6142857145 Combine like terms: -0.6142857145 + 0.6142857145 = 0.0000000000 0.0000000000 + x = -2.111629606 + 0.6142857145 x = -2.111629606 + 0.6142857145 Combine like terms: -2.111629606 + 0.6142857145 = -1.4973438915 x = -1.4973438915 Simplifying x = -1.4973438915Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7259153205, -1.4973438915}
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