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Simplifying -4.9x2 + 28x + 28 = 0 Reorder the terms: 28 + 28x + -4.9x2 = 0 Solving 28 + 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'. -5.714285714 + -5.714285714x + x2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + -5.714285714x + 5.714285714 + x2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + -5.714285714x + x2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + -5.714285714x + x2 = 0 + 5.714285714 -5.714285714x + x2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 -5.714285714x + x2 = 5.714285714 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 = 5.714285714 + 8.163265305 Reorder the terms: 8.163265305 + -5.714285714x + x2 = 5.714285714 + 8.163265305 Combine like terms: 5.714285714 + 8.163265305 = 13.877551019 8.163265305 + -5.714285714x + x2 = 13.877551019 Factor a perfect square on the left side: (x + -2.857142857)(x + -2.857142857) = 13.877551019 Calculate the square root of the right side: 3.725258517 Break this problem into two subproblems by setting (x + -2.857142857) equal to 3.725258517 and -3.725258517.Subproblem 1
x + -2.857142857 = 3.725258517 Simplifying x + -2.857142857 = 3.725258517 Reorder the terms: -2.857142857 + x = 3.725258517 Solving -2.857142857 + x = 3.725258517 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 = 3.725258517 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + x = 3.725258517 + 2.857142857 x = 3.725258517 + 2.857142857 Combine like terms: 3.725258517 + 2.857142857 = 6.582401374 x = 6.582401374 Simplifying x = 6.582401374Subproblem 2
x + -2.857142857 = -3.725258517 Simplifying x + -2.857142857 = -3.725258517 Reorder the terms: -2.857142857 + x = -3.725258517 Solving -2.857142857 + x = -3.725258517 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 = -3.725258517 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + x = -3.725258517 + 2.857142857 x = -3.725258517 + 2.857142857 Combine like terms: -3.725258517 + 2.857142857 = -0.86811566 x = -0.86811566 Simplifying x = -0.86811566Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.582401374, -0.86811566}
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