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Simplifying 20 = 42x + -4.9x2 Solving 20 = 42x + -4.9x2 Solving for variable 'x'. Reorder the terms: 20 + -42x + 4.9x2 = 42x + -42x + -4.9x2 + 4.9x2 Combine like terms: 42x + -42x = 0 20 + -42x + 4.9x2 = 0 + -4.9x2 + 4.9x2 20 + -42x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 20 + -42x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 4.081632653 + -8.571428571x + x2 = 0 Move the constant term to the right: Add '-4.081632653' to each side of the equation. 4.081632653 + -8.571428571x + -4.081632653 + x2 = 0 + -4.081632653 Reorder the terms: 4.081632653 + -4.081632653 + -8.571428571x + x2 = 0 + -4.081632653 Combine like terms: 4.081632653 + -4.081632653 = 0.000000000 0.000000000 + -8.571428571x + x2 = 0 + -4.081632653 -8.571428571x + x2 = 0 + -4.081632653 Combine like terms: 0 + -4.081632653 = -4.081632653 -8.571428571x + x2 = -4.081632653 The x term is -8.571428571x. Take half its coefficient (-4.285714286). Square it (18.36734694) and add it to both sides. Add '18.36734694' to each side of the equation. -8.571428571x + 18.36734694 + x2 = -4.081632653 + 18.36734694 Reorder the terms: 18.36734694 + -8.571428571x + x2 = -4.081632653 + 18.36734694 Combine like terms: -4.081632653 + 18.36734694 = 14.285714287 18.36734694 + -8.571428571x + x2 = 14.285714287 Factor a perfect square on the left side: (x + -4.285714286)(x + -4.285714286) = 14.285714287 Calculate the square root of the right side: 3.77964473 Break this problem into two subproblems by setting (x + -4.285714286) equal to 3.77964473 and -3.77964473.Subproblem 1
x + -4.285714286 = 3.77964473 Simplifying x + -4.285714286 = 3.77964473 Reorder the terms: -4.285714286 + x = 3.77964473 Solving -4.285714286 + x = 3.77964473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + x = 3.77964473 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + x = 3.77964473 + 4.285714286 x = 3.77964473 + 4.285714286 Combine like terms: 3.77964473 + 4.285714286 = 8.065359016 x = 8.065359016 Simplifying x = 8.065359016Subproblem 2
x + -4.285714286 = -3.77964473 Simplifying x + -4.285714286 = -3.77964473 Reorder the terms: -4.285714286 + x = -3.77964473 Solving -4.285714286 + x = -3.77964473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + x = -3.77964473 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + x = -3.77964473 + 4.285714286 x = -3.77964473 + 4.285714286 Combine like terms: -3.77964473 + 4.285714286 = 0.506069556 x = 0.506069556 Simplifying x = 0.506069556Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.065359016, 0.506069556}
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