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Simplifying -4.9x2 + -28x + 80 = 0 Reorder the terms: 80 + -28x + -4.9x2 = 0 Solving 80 + -28x + -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'. -16.32653061 + 5.714285714x + x2 = 0 Move the constant term to the right: Add '16.32653061' to each side of the equation. -16.32653061 + 5.714285714x + 16.32653061 + x2 = 0 + 16.32653061 Reorder the terms: -16.32653061 + 16.32653061 + 5.714285714x + x2 = 0 + 16.32653061 Combine like terms: -16.32653061 + 16.32653061 = 0.00000000 0.00000000 + 5.714285714x + x2 = 0 + 16.32653061 5.714285714x + x2 = 0 + 16.32653061 Combine like terms: 0 + 16.32653061 = 16.32653061 5.714285714x + x2 = 16.32653061 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 = 16.32653061 + 8.163265305 Reorder the terms: 8.163265305 + 5.714285714x + x2 = 16.32653061 + 8.163265305 Combine like terms: 16.32653061 + 8.163265305 = 24.489795915 8.163265305 + 5.714285714x + x2 = 24.489795915 Factor a perfect square on the left side: (x + 2.857142857)(x + 2.857142857) = 24.489795915 Calculate the square root of the right side: 4.948716593 Break this problem into two subproblems by setting (x + 2.857142857) equal to 4.948716593 and -4.948716593.Subproblem 1
x + 2.857142857 = 4.948716593 Simplifying x + 2.857142857 = 4.948716593 Reorder the terms: 2.857142857 + x = 4.948716593 Solving 2.857142857 + x = 4.948716593 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 = 4.948716593 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + x = 4.948716593 + -2.857142857 x = 4.948716593 + -2.857142857 Combine like terms: 4.948716593 + -2.857142857 = 2.091573736 x = 2.091573736 Simplifying x = 2.091573736Subproblem 2
x + 2.857142857 = -4.948716593 Simplifying x + 2.857142857 = -4.948716593 Reorder the terms: 2.857142857 + x = -4.948716593 Solving 2.857142857 + x = -4.948716593 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 = -4.948716593 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + x = -4.948716593 + -2.857142857 x = -4.948716593 + -2.857142857 Combine like terms: -4.948716593 + -2.857142857 = -7.80585945 x = -7.80585945 Simplifying x = -7.80585945Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.091573736, -7.80585945}
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