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Simplifying 7x2 + 10x + -9 = 0 Reorder the terms: -9 + 10x + 7x2 = 0 Solving -9 + 10x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 1.428571429x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 1.428571429x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 1.428571429x + x2 = 0 + 1.285714286 1.428571429x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 1.428571429x + x2 = 1.285714286 The x term is 1.428571429x. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429x + 0.5102040819 + x2 = 1.285714286 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 1.285714286 + 0.5102040819 Combine like terms: 1.285714286 + 0.5102040819 = 1.7959183679 0.5102040819 + 1.428571429x + x2 = 1.7959183679 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 1.7959183679 Calculate the square root of the right side: 1.340118789 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 1.340118789 and -1.340118789.Subproblem 1
x + 0.7142857145 = 1.340118789 Simplifying x + 0.7142857145 = 1.340118789 Reorder the terms: 0.7142857145 + x = 1.340118789 Solving 0.7142857145 + x = 1.340118789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 1.340118789 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 1.340118789 + -0.7142857145 x = 1.340118789 + -0.7142857145 Combine like terms: 1.340118789 + -0.7142857145 = 0.6258330745 x = 0.6258330745 Simplifying x = 0.6258330745Subproblem 2
x + 0.7142857145 = -1.340118789 Simplifying x + 0.7142857145 = -1.340118789 Reorder the terms: 0.7142857145 + x = -1.340118789 Solving 0.7142857145 + x = -1.340118789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -1.340118789 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -1.340118789 + -0.7142857145 x = -1.340118789 + -0.7142857145 Combine like terms: -1.340118789 + -0.7142857145 = -2.0544045035 x = -2.0544045035 Simplifying x = -2.0544045035Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6258330745, -2.0544045035}
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