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Simplifying 20x2 + -77x + -28 = 0 Reorder the terms: -28 + -77x + 20x2 = 0 Solving -28 + -77x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1.4 + -3.85x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -3.85x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -3.85x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -3.85x + x2 = 0 + 1.4 -3.85x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -3.85x + x2 = 1.4 The x term is -3.85x. Take half its coefficient (-1.925). Square it (3.705625) and add it to both sides. Add '3.705625' to each side of the equation. -3.85x + 3.705625 + x2 = 1.4 + 3.705625 Reorder the terms: 3.705625 + -3.85x + x2 = 1.4 + 3.705625 Combine like terms: 1.4 + 3.705625 = 5.105625 3.705625 + -3.85x + x2 = 5.105625 Factor a perfect square on the left side: (x + -1.925)(x + -1.925) = 5.105625 Calculate the square root of the right side: 2.259563011 Break this problem into two subproblems by setting (x + -1.925) equal to 2.259563011 and -2.259563011.Subproblem 1
x + -1.925 = 2.259563011 Simplifying x + -1.925 = 2.259563011 Reorder the terms: -1.925 + x = 2.259563011 Solving -1.925 + x = 2.259563011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.925' to each side of the equation. -1.925 + 1.925 + x = 2.259563011 + 1.925 Combine like terms: -1.925 + 1.925 = 0.000 0.000 + x = 2.259563011 + 1.925 x = 2.259563011 + 1.925 Combine like terms: 2.259563011 + 1.925 = 4.184563011 x = 4.184563011 Simplifying x = 4.184563011Subproblem 2
x + -1.925 = -2.259563011 Simplifying x + -1.925 = -2.259563011 Reorder the terms: -1.925 + x = -2.259563011 Solving -1.925 + x = -2.259563011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.925' to each side of the equation. -1.925 + 1.925 + x = -2.259563011 + 1.925 Combine like terms: -1.925 + 1.925 = 0.000 0.000 + x = -2.259563011 + 1.925 x = -2.259563011 + 1.925 Combine like terms: -2.259563011 + 1.925 = -0.334563011 x = -0.334563011 Simplifying x = -0.334563011Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.184563011, -0.334563011}
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