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Simplifying 0 = 4.9x2 + 28x + 2 Reorder the terms: 0 = 2 + 28x + 4.9x2 Solving 0 = 2 + 28x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -28x + -4.9x2 = 2 + 28x + 4.9x2 + -2 + -28x + -4.9x2 Reorder the terms: -2 + -28x + -4.9x2 = 2 + -2 + 28x + -28x + 4.9x2 + -4.9x2 Combine like terms: 2 + -2 = 0 -2 + -28x + -4.9x2 = 0 + 28x + -28x + 4.9x2 + -4.9x2 -2 + -28x + -4.9x2 = 28x + -28x + 4.9x2 + -4.9x2 Combine like terms: 28x + -28x = 0 -2 + -28x + -4.9x2 = 0 + 4.9x2 + -4.9x2 -2 + -28x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 -2 + -28x + -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'. 0.4081632653 + 5.714285714x + x2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + 5.714285714x + -0.4081632653 + x2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + 5.714285714x + x2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + 5.714285714x + x2 = 0 + -0.4081632653 5.714285714x + x2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 5.714285714x + x2 = -0.4081632653 The x term is 5.714285714x. Take half its coefficient (2.857142857). Square it (8.163265305) and add it to both sides. Add '8.163265305' to each side of the equation. 5.714285714x + 8.163265305 + x2 = -0.4081632653 + 8.163265305 Reorder the terms: 8.163265305 + 5.714285714x + x2 = -0.4081632653 + 8.163265305 Combine like terms: -0.4081632653 + 8.163265305 = 7.7551020397 8.163265305 + 5.714285714x + x2 = 7.7551020397 Factor a perfect square on the left side: (x + 2.857142857)(x + 2.857142857) = 7.7551020397 Calculate the square root of the right side: 2.784798384 Break this problem into two subproblems by setting (x + 2.857142857) equal to 2.784798384 and -2.784798384.Subproblem 1
x + 2.857142857 = 2.784798384 Simplifying x + 2.857142857 = 2.784798384 Reorder the terms: 2.857142857 + x = 2.784798384 Solving 2.857142857 + x = 2.784798384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.857142857' to each side of the equation. 2.857142857 + -2.857142857 + x = 2.784798384 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + x = 2.784798384 + -2.857142857 x = 2.784798384 + -2.857142857 Combine like terms: 2.784798384 + -2.857142857 = -0.072344473 x = -0.072344473 Simplifying x = -0.072344473Subproblem 2
x + 2.857142857 = -2.784798384 Simplifying x + 2.857142857 = -2.784798384 Reorder the terms: 2.857142857 + x = -2.784798384 Solving 2.857142857 + x = -2.784798384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.857142857' to each side of the equation. 2.857142857 + -2.857142857 + x = -2.784798384 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + x = -2.784798384 + -2.857142857 x = -2.784798384 + -2.857142857 Combine like terms: -2.784798384 + -2.857142857 = -5.641941241 x = -5.641941241 Simplifying x = -5.641941241Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.072344473, -5.641941241}
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