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Simplifying 7x2 + -25x + 5 = 0 Reorder the terms: 5 + -25x + 7x2 = 0 Solving 5 + -25x + 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'. 0.7142857143 + -3.571428571x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -3.571428571x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -3.571428571x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -3.571428571x + x2 = 0 + -0.7142857143 -3.571428571x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -3.571428571x + x2 = -0.7142857143 The x term is -3.571428571x. Take half its coefficient (-1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. -3.571428571x + 3.188775511 + x2 = -0.7142857143 + 3.188775511 Reorder the terms: 3.188775511 + -3.571428571x + x2 = -0.7142857143 + 3.188775511 Combine like terms: -0.7142857143 + 3.188775511 = 2.4744897967 3.188775511 + -3.571428571x + x2 = 2.4744897967 Factor a perfect square on the left side: (x + -1.785714286)(x + -1.785714286) = 2.4744897967 Calculate the square root of the right side: 1.573051111 Break this problem into two subproblems by setting (x + -1.785714286) equal to 1.573051111 and -1.573051111.Subproblem 1
x + -1.785714286 = 1.573051111 Simplifying x + -1.785714286 = 1.573051111 Reorder the terms: -1.785714286 + x = 1.573051111 Solving -1.785714286 + x = 1.573051111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = 1.573051111 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = 1.573051111 + 1.785714286 x = 1.573051111 + 1.785714286 Combine like terms: 1.573051111 + 1.785714286 = 3.358765397 x = 3.358765397 Simplifying x = 3.358765397Subproblem 2
x + -1.785714286 = -1.573051111 Simplifying x + -1.785714286 = -1.573051111 Reorder the terms: -1.785714286 + x = -1.573051111 Solving -1.785714286 + x = -1.573051111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = -1.573051111 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = -1.573051111 + 1.785714286 x = -1.573051111 + 1.785714286 Combine like terms: -1.573051111 + 1.785714286 = 0.212663175 x = 0.212663175 Simplifying x = 0.212663175Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.358765397, 0.212663175}
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