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Simplifying 7x2 + -25x + 2 = 0 Reorder the terms: 2 + -25x + 7x2 = 0 Solving 2 + -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'. 0.2857142857 + -3.571428571x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + -3.571428571x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + -3.571428571x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + -3.571428571x + x2 = 0 + -0.2857142857 -3.571428571x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 -3.571428571x + x2 = -0.2857142857 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 = -0.2857142857 + 3.188775511 Reorder the terms: 3.188775511 + -3.571428571x + x2 = -0.2857142857 + 3.188775511 Combine like terms: -0.2857142857 + 3.188775511 = 2.9030612253 3.188775511 + -3.571428571x + x2 = 2.9030612253 Factor a perfect square on the left side: (x + -1.785714286)(x + -1.785714286) = 2.9030612253 Calculate the square root of the right side: 1.703837206 Break this problem into two subproblems by setting (x + -1.785714286) equal to 1.703837206 and -1.703837206.Subproblem 1
x + -1.785714286 = 1.703837206 Simplifying x + -1.785714286 = 1.703837206 Reorder the terms: -1.785714286 + x = 1.703837206 Solving -1.785714286 + x = 1.703837206 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 = 1.703837206 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = 1.703837206 + 1.785714286 x = 1.703837206 + 1.785714286 Combine like terms: 1.703837206 + 1.785714286 = 3.489551492 x = 3.489551492 Simplifying x = 3.489551492Subproblem 2
x + -1.785714286 = -1.703837206 Simplifying x + -1.785714286 = -1.703837206 Reorder the terms: -1.785714286 + x = -1.703837206 Solving -1.785714286 + x = -1.703837206 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 = -1.703837206 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = -1.703837206 + 1.785714286 x = -1.703837206 + 1.785714286 Combine like terms: -1.703837206 + 1.785714286 = 0.08187708 x = 0.08187708 Simplifying x = 0.08187708Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.489551492, 0.08187708}
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