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Simplifying 7x2 + -39x + 2 = 0 Reorder the terms: 2 + -39x + 7x2 = 0 Solving 2 + -39x + 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 + -5.571428571x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + -5.571428571x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + -5.571428571x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + -5.571428571x + x2 = 0 + -0.2857142857 -5.571428571x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 -5.571428571x + x2 = -0.2857142857 The x term is -5.571428571x. Take half its coefficient (-2.785714286). Square it (7.760204083) and add it to both sides. Add '7.760204083' to each side of the equation. -5.571428571x + 7.760204083 + x2 = -0.2857142857 + 7.760204083 Reorder the terms: 7.760204083 + -5.571428571x + x2 = -0.2857142857 + 7.760204083 Combine like terms: -0.2857142857 + 7.760204083 = 7.4744897973 7.760204083 + -5.571428571x + x2 = 7.4744897973 Factor a perfect square on the left side: (x + -2.785714286)(x + -2.785714286) = 7.4744897973 Calculate the square root of the right side: 2.733951316 Break this problem into two subproblems by setting (x + -2.785714286) equal to 2.733951316 and -2.733951316.Subproblem 1
x + -2.785714286 = 2.733951316 Simplifying x + -2.785714286 = 2.733951316 Reorder the terms: -2.785714286 + x = 2.733951316 Solving -2.785714286 + x = 2.733951316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.785714286' to each side of the equation. -2.785714286 + 2.785714286 + x = 2.733951316 + 2.785714286 Combine like terms: -2.785714286 + 2.785714286 = 0.000000000 0.000000000 + x = 2.733951316 + 2.785714286 x = 2.733951316 + 2.785714286 Combine like terms: 2.733951316 + 2.785714286 = 5.519665602 x = 5.519665602 Simplifying x = 5.519665602Subproblem 2
x + -2.785714286 = -2.733951316 Simplifying x + -2.785714286 = -2.733951316 Reorder the terms: -2.785714286 + x = -2.733951316 Solving -2.785714286 + x = -2.733951316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.785714286' to each side of the equation. -2.785714286 + 2.785714286 + x = -2.733951316 + 2.785714286 Combine like terms: -2.785714286 + 2.785714286 = 0.000000000 0.000000000 + x = -2.733951316 + 2.785714286 x = -2.733951316 + 2.785714286 Combine like terms: -2.733951316 + 2.785714286 = 0.05176297 x = 0.05176297 Simplifying x = 0.05176297Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.519665602, 0.05176297}
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