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Simplifying 20x2 + -68x + -27 = 0 Reorder the terms: -27 + -68x + 20x2 = 0 Solving -27 + -68x + 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'. -1.35 + -3.4x + x2 = 0 Move the constant term to the right: Add '1.35' to each side of the equation. -1.35 + -3.4x + 1.35 + x2 = 0 + 1.35 Reorder the terms: -1.35 + 1.35 + -3.4x + x2 = 0 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + -3.4x + x2 = 0 + 1.35 -3.4x + x2 = 0 + 1.35 Combine like terms: 0 + 1.35 = 1.35 -3.4x + x2 = 1.35 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = 1.35 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 1.35 + 2.89 Combine like terms: 1.35 + 2.89 = 4.24 2.89 + -3.4x + x2 = 4.24 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 4.24 Calculate the square root of the right side: 2.059126028 Break this problem into two subproblems by setting (x + -1.7) equal to 2.059126028 and -2.059126028.Subproblem 1
x + -1.7 = 2.059126028 Simplifying x + -1.7 = 2.059126028 Reorder the terms: -1.7 + x = 2.059126028 Solving -1.7 + x = 2.059126028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 2.059126028 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 2.059126028 + 1.7 x = 2.059126028 + 1.7 Combine like terms: 2.059126028 + 1.7 = 3.759126028 x = 3.759126028 Simplifying x = 3.759126028Subproblem 2
x + -1.7 = -2.059126028 Simplifying x + -1.7 = -2.059126028 Reorder the terms: -1.7 + x = -2.059126028 Solving -1.7 + x = -2.059126028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -2.059126028 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -2.059126028 + 1.7 x = -2.059126028 + 1.7 Combine like terms: -2.059126028 + 1.7 = -0.359126028 x = -0.359126028 Simplifying x = -0.359126028Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.759126028, -0.359126028}
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