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Simplifying -0.71x2 + -0.52x + 0.25 = 0 Reorder the terms: 0.25 + -0.52x + -0.71x2 = 0 Solving 0.25 + -0.52x + -0.71x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.71 the coefficient of the squared term: Divide each side by '-0.71'. -0.3521126761 + 0.7323943662x + x2 = 0 Move the constant term to the right: Add '0.3521126761' to each side of the equation. -0.3521126761 + 0.7323943662x + 0.3521126761 + x2 = 0 + 0.3521126761 Reorder the terms: -0.3521126761 + 0.3521126761 + 0.7323943662x + x2 = 0 + 0.3521126761 Combine like terms: -0.3521126761 + 0.3521126761 = 0.0000000000 0.0000000000 + 0.7323943662x + x2 = 0 + 0.3521126761 0.7323943662x + x2 = 0 + 0.3521126761 Combine like terms: 0 + 0.3521126761 = 0.3521126761 0.7323943662x + x2 = 0.3521126761 The x term is 0.7323943662x. Take half its coefficient (0.3661971831). Square it (0.1341003769) and add it to both sides. Add '0.1341003769' to each side of the equation. 0.7323943662x + 0.1341003769 + x2 = 0.3521126761 + 0.1341003769 Reorder the terms: 0.1341003769 + 0.7323943662x + x2 = 0.3521126761 + 0.1341003769 Combine like terms: 0.3521126761 + 0.1341003769 = 0.486213053 0.1341003769 + 0.7323943662x + x2 = 0.486213053 Factor a perfect square on the left side: (x + 0.3661971831)(x + 0.3661971831) = 0.486213053 Calculate the square root of the right side: 0.697289791 Break this problem into two subproblems by setting (x + 0.3661971831) equal to 0.697289791 and -0.697289791.Subproblem 1
x + 0.3661971831 = 0.697289791 Simplifying x + 0.3661971831 = 0.697289791 Reorder the terms: 0.3661971831 + x = 0.697289791 Solving 0.3661971831 + x = 0.697289791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3661971831' to each side of the equation. 0.3661971831 + -0.3661971831 + x = 0.697289791 + -0.3661971831 Combine like terms: 0.3661971831 + -0.3661971831 = 0.0000000000 0.0000000000 + x = 0.697289791 + -0.3661971831 x = 0.697289791 + -0.3661971831 Combine like terms: 0.697289791 + -0.3661971831 = 0.3310926079 x = 0.3310926079 Simplifying x = 0.3310926079Subproblem 2
x + 0.3661971831 = -0.697289791 Simplifying x + 0.3661971831 = -0.697289791 Reorder the terms: 0.3661971831 + x = -0.697289791 Solving 0.3661971831 + x = -0.697289791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3661971831' to each side of the equation. 0.3661971831 + -0.3661971831 + x = -0.697289791 + -0.3661971831 Combine like terms: 0.3661971831 + -0.3661971831 = 0.0000000000 0.0000000000 + x = -0.697289791 + -0.3661971831 x = -0.697289791 + -0.3661971831 Combine like terms: -0.697289791 + -0.3661971831 = -1.0634869741 x = -1.0634869741 Simplifying x = -1.0634869741Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3310926079, -1.0634869741}
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