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Simplifying -7x2 + 10x + 16 = 0 Reorder the terms: 16 + 10x + -7x2 = 0 Solving 16 + 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'. -2.285714286 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + -1.428571429x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + -1.428571429x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + -1.428571429x + x2 = 0 + 2.285714286 -1.428571429x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 -1.428571429x + x2 = 2.285714286 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 = 2.285714286 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 2.285714286 + 0.5102040819 Combine like terms: 2.285714286 + 0.5102040819 = 2.7959183679 0.5102040819 + -1.428571429x + x2 = 2.7959183679 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 2.7959183679 Calculate the square root of the right side: 1.672099987 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 1.672099987 and -1.672099987.Subproblem 1
x + -0.7142857145 = 1.672099987 Simplifying x + -0.7142857145 = 1.672099987 Reorder the terms: -0.7142857145 + x = 1.672099987 Solving -0.7142857145 + x = 1.672099987 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 = 1.672099987 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 1.672099987 + 0.7142857145 x = 1.672099987 + 0.7142857145 Combine like terms: 1.672099987 + 0.7142857145 = 2.3863857015 x = 2.3863857015 Simplifying x = 2.3863857015Subproblem 2
x + -0.7142857145 = -1.672099987 Simplifying x + -0.7142857145 = -1.672099987 Reorder the terms: -0.7142857145 + x = -1.672099987 Solving -0.7142857145 + x = -1.672099987 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 = -1.672099987 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -1.672099987 + 0.7142857145 x = -1.672099987 + 0.7142857145 Combine like terms: -1.672099987 + 0.7142857145 = -0.9578142725 x = -0.9578142725 Simplifying x = -0.9578142725Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3863857015, -0.9578142725}
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