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Simplifying 14x2 + 81x + -100 = 0 Reorder the terms: -100 + 81x + 14x2 = 0 Solving -100 + 81x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -7.142857143 + 5.785714286x + x2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + 5.785714286x + 7.142857143 + x2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + 5.785714286x + x2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + 5.785714286x + x2 = 0 + 7.142857143 5.785714286x + x2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 5.785714286x + x2 = 7.142857143 The x term is 5.785714286x. Take half its coefficient (2.892857143). Square it (8.368622450) and add it to both sides. Add '8.368622450' to each side of the equation. 5.785714286x + 8.368622450 + x2 = 7.142857143 + 8.368622450 Reorder the terms: 8.368622450 + 5.785714286x + x2 = 7.142857143 + 8.368622450 Combine like terms: 7.142857143 + 8.368622450 = 15.511479593 8.368622450 + 5.785714286x + x2 = 15.511479593 Factor a perfect square on the left side: (x + 2.892857143)(x + 2.892857143) = 15.511479593 Calculate the square root of the right side: 3.938461577 Break this problem into two subproblems by setting (x + 2.892857143) equal to 3.938461577 and -3.938461577.Subproblem 1
x + 2.892857143 = 3.938461577 Simplifying x + 2.892857143 = 3.938461577 Reorder the terms: 2.892857143 + x = 3.938461577 Solving 2.892857143 + x = 3.938461577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.892857143' to each side of the equation. 2.892857143 + -2.892857143 + x = 3.938461577 + -2.892857143 Combine like terms: 2.892857143 + -2.892857143 = 0.000000000 0.000000000 + x = 3.938461577 + -2.892857143 x = 3.938461577 + -2.892857143 Combine like terms: 3.938461577 + -2.892857143 = 1.045604434 x = 1.045604434 Simplifying x = 1.045604434Subproblem 2
x + 2.892857143 = -3.938461577 Simplifying x + 2.892857143 = -3.938461577 Reorder the terms: 2.892857143 + x = -3.938461577 Solving 2.892857143 + x = -3.938461577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.892857143' to each side of the equation. 2.892857143 + -2.892857143 + x = -3.938461577 + -2.892857143 Combine like terms: 2.892857143 + -2.892857143 = 0.000000000 0.000000000 + x = -3.938461577 + -2.892857143 x = -3.938461577 + -2.892857143 Combine like terms: -3.938461577 + -2.892857143 = -6.83131872 x = -6.83131872 Simplifying x = -6.83131872Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.045604434, -6.83131872}
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