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Simplifying (7x2) + (14x) + 6 = 0 Reorder the terms: 6 + (14x) + (7x2) = 0 Solving 6 + (14x) + (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'. 0.8571428571 + (2x) + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + (2x) + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + (2x) + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + (2x) + x2 = 0 + -0.8571428571 (2x) + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 (2x) + x2 = -0.8571428571 The x term is (2x). Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. (2x) + 1 + x2 = -0.8571428571 + 1 Reorder the terms: 1 + (2x) + x2 = -0.8571428571 + 1 Combine like terms: -0.8571428571 + 1 = 0.1428571429 1 + (2x) + x2 = 0.1428571429 Factor a perfect square on the left side: ((x) + 1)((x) + 1) = 0.1428571429 Calculate the square root of the right side: 0.377964473 Break this problem into two subproblems by setting ((x) + 1) equal to 0.377964473 and -0.377964473.Subproblem 1
(x) + 1 = 0.377964473 Simplifying (x) + 1 = 0.377964473 x + 1 = 0.377964473 Reorder the terms: 1 + x = 0.377964473 Solving 1 + x = 0.377964473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.377964473 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.377964473 + -1 x = 0.377964473 + -1 Combine like terms: 0.377964473 + -1 = -0.622035527 x = -0.622035527 Simplifying x = -0.622035527Subproblem 2
(x) + 1 = -0.377964473 Simplifying (x) + 1 = -0.377964473 x + 1 = -0.377964473 Reorder the terms: 1 + x = -0.377964473 Solving 1 + x = -0.377964473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.377964473 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.377964473 + -1 x = -0.377964473 + -1 Combine like terms: -0.377964473 + -1 = -1.377964473 x = -1.377964473 Simplifying x = -1.377964473Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.622035527, -1.377964473}
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