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Simplifying 4.9x2 + 5.25x + -20 = 0 Reorder the terms: -20 + 5.25x + 4.9x2 = 0 Solving -20 + 5.25x + 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 + 1.071428571x + x2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + 1.071428571x + 4.081632653 + x2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + 1.071428571x + x2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + 1.071428571x + x2 = 0 + 4.081632653 1.071428571x + x2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 1.071428571x + x2 = 4.081632653 The x term is 1.071428571x. Take half its coefficient (0.5357142855). Square it (0.2869897957) and add it to both sides. Add '0.2869897957' to each side of the equation. 1.071428571x + 0.2869897957 + x2 = 4.081632653 + 0.2869897957 Reorder the terms: 0.2869897957 + 1.071428571x + x2 = 4.081632653 + 0.2869897957 Combine like terms: 4.081632653 + 0.2869897957 = 4.3686224487 0.2869897957 + 1.071428571x + x2 = 4.3686224487 Factor a perfect square on the left side: (x + 0.5357142855)(x + 0.5357142855) = 4.3686224487 Calculate the square root of the right side: 2.090124984 Break this problem into two subproblems by setting (x + 0.5357142855) equal to 2.090124984 and -2.090124984.Subproblem 1
x + 0.5357142855 = 2.090124984 Simplifying x + 0.5357142855 = 2.090124984 Reorder the terms: 0.5357142855 + x = 2.090124984 Solving 0.5357142855 + x = 2.090124984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5357142855' to each side of the equation. 0.5357142855 + -0.5357142855 + x = 2.090124984 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + x = 2.090124984 + -0.5357142855 x = 2.090124984 + -0.5357142855 Combine like terms: 2.090124984 + -0.5357142855 = 1.5544106985 x = 1.5544106985 Simplifying x = 1.5544106985Subproblem 2
x + 0.5357142855 = -2.090124984 Simplifying x + 0.5357142855 = -2.090124984 Reorder the terms: 0.5357142855 + x = -2.090124984 Solving 0.5357142855 + x = -2.090124984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5357142855' to each side of the equation. 0.5357142855 + -0.5357142855 + x = -2.090124984 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + x = -2.090124984 + -0.5357142855 x = -2.090124984 + -0.5357142855 Combine like terms: -2.090124984 + -0.5357142855 = -2.6258392695 x = -2.6258392695 Simplifying x = -2.6258392695Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5544106985, -2.6258392695}
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