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Simplifying 5x2 + -77x + 89 = 0 Reorder the terms: 89 + -77x + 5x2 = 0 Solving 89 + -77x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 17.8 + -15.4x + x2 = 0 Move the constant term to the right: Add '-17.8' to each side of the equation. 17.8 + -15.4x + -17.8 + x2 = 0 + -17.8 Reorder the terms: 17.8 + -17.8 + -15.4x + x2 = 0 + -17.8 Combine like terms: 17.8 + -17.8 = 0.0 0.0 + -15.4x + x2 = 0 + -17.8 -15.4x + x2 = 0 + -17.8 Combine like terms: 0 + -17.8 = -17.8 -15.4x + x2 = -17.8 The x term is -15.4x. Take half its coefficient (-7.7). Square it (59.29) and add it to both sides. Add '59.29' to each side of the equation. -15.4x + 59.29 + x2 = -17.8 + 59.29 Reorder the terms: 59.29 + -15.4x + x2 = -17.8 + 59.29 Combine like terms: -17.8 + 59.29 = 41.49 59.29 + -15.4x + x2 = 41.49 Factor a perfect square on the left side: (x + -7.7)(x + -7.7) = 41.49 Calculate the square root of the right side: 6.441273166 Break this problem into two subproblems by setting (x + -7.7) equal to 6.441273166 and -6.441273166.Subproblem 1
x + -7.7 = 6.441273166 Simplifying x + -7.7 = 6.441273166 Reorder the terms: -7.7 + x = 6.441273166 Solving -7.7 + x = 6.441273166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.7' to each side of the equation. -7.7 + 7.7 + x = 6.441273166 + 7.7 Combine like terms: -7.7 + 7.7 = 0.0 0.0 + x = 6.441273166 + 7.7 x = 6.441273166 + 7.7 Combine like terms: 6.441273166 + 7.7 = 14.141273166 x = 14.141273166 Simplifying x = 14.141273166Subproblem 2
x + -7.7 = -6.441273166 Simplifying x + -7.7 = -6.441273166 Reorder the terms: -7.7 + x = -6.441273166 Solving -7.7 + x = -6.441273166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.7' to each side of the equation. -7.7 + 7.7 + x = -6.441273166 + 7.7 Combine like terms: -7.7 + 7.7 = 0.0 0.0 + x = -6.441273166 + 7.7 x = -6.441273166 + 7.7 Combine like terms: -6.441273166 + 7.7 = 1.258726834 x = 1.258726834 Simplifying x = 1.258726834Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.141273166, 1.258726834}
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