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Simplifying 7x2 + 18x + 4 = 0 Reorder the terms: 4 + 18x + 7x2 = 0 Solving 4 + 18x + 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'. 0.5714285714 + 2.571428571x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + 2.571428571x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + 2.571428571x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + 2.571428571x + x2 = 0 + -0.5714285714 2.571428571x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 2.571428571x + x2 = -0.5714285714 The x term is 2.571428571x. Take half its coefficient (1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. 2.571428571x + 1.653061225 + x2 = -0.5714285714 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571x + x2 = -0.5714285714 + 1.653061225 Combine like terms: -0.5714285714 + 1.653061225 = 1.0816326536 1.653061225 + 2.571428571x + x2 = 1.0816326536 Factor a perfect square on the left side: (x + 1.285714286)(x + 1.285714286) = 1.0816326536 Calculate the square root of the right side: 1.040015699 Break this problem into two subproblems by setting (x + 1.285714286) equal to 1.040015699 and -1.040015699.Subproblem 1
x + 1.285714286 = 1.040015699 Simplifying x + 1.285714286 = 1.040015699 Reorder the terms: 1.285714286 + x = 1.040015699 Solving 1.285714286 + x = 1.040015699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + x = 1.040015699 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = 1.040015699 + -1.285714286 x = 1.040015699 + -1.285714286 Combine like terms: 1.040015699 + -1.285714286 = -0.245698587 x = -0.245698587 Simplifying x = -0.245698587Subproblem 2
x + 1.285714286 = -1.040015699 Simplifying x + 1.285714286 = -1.040015699 Reorder the terms: 1.285714286 + x = -1.040015699 Solving 1.285714286 + x = -1.040015699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + x = -1.040015699 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = -1.040015699 + -1.285714286 x = -1.040015699 + -1.285714286 Combine like terms: -1.040015699 + -1.285714286 = -2.325729985 x = -2.325729985 Simplifying x = -2.325729985Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.245698587, -2.325729985}
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