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Simplifying 20 = -12x + 4.9x2 Solving 20 = -12x + 4.9x2 Solving for variable 'x'. Reorder the terms: 20 + 12x + -4.9x2 = -12x + 12x + 4.9x2 + -4.9x2 Combine like terms: -12x + 12x = 0 20 + 12x + -4.9x2 = 0 + 4.9x2 + -4.9x2 20 + 12x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 20 + 12x + -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 + -2.448979592x + x2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + -2.448979592x + 4.081632653 + x2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + -2.448979592x + x2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + -2.448979592x + x2 = 0 + 4.081632653 -2.448979592x + x2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 -2.448979592x + x2 = 4.081632653 The x term is -2.448979592x. Take half its coefficient (-1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. -2.448979592x + 1.499375261 + x2 = 4.081632653 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592x + x2 = 4.081632653 + 1.499375261 Combine like terms: 4.081632653 + 1.499375261 = 5.581007914 1.499375261 + -2.448979592x + x2 = 5.581007914 Factor a perfect square on the left side: (x + -1.224489796)(x + -1.224489796) = 5.581007914 Calculate the square root of the right side: 2.362415695 Break this problem into two subproblems by setting (x + -1.224489796) equal to 2.362415695 and -2.362415695.Subproblem 1
x + -1.224489796 = 2.362415695 Simplifying x + -1.224489796 = 2.362415695 Reorder the terms: -1.224489796 + x = 2.362415695 Solving -1.224489796 + x = 2.362415695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + x = 2.362415695 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = 2.362415695 + 1.224489796 x = 2.362415695 + 1.224489796 Combine like terms: 2.362415695 + 1.224489796 = 3.586905491 x = 3.586905491 Simplifying x = 3.586905491Subproblem 2
x + -1.224489796 = -2.362415695 Simplifying x + -1.224489796 = -2.362415695 Reorder the terms: -1.224489796 + x = -2.362415695 Solving -1.224489796 + x = -2.362415695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + x = -2.362415695 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = -2.362415695 + 1.224489796 x = -2.362415695 + 1.224489796 Combine like terms: -2.362415695 + 1.224489796 = -1.137925899 x = -1.137925899 Simplifying x = -1.137925899Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.586905491, -1.137925899}
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