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Simplifying 7x2 + -18x + -5 = 0 Reorder the terms: -5 + -18x + 7x2 = 0 Solving -5 + -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'. -0.7142857143 + -2.571428571x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -2.571428571x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -2.571428571x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -2.571428571x + x2 = 0 + 0.7142857143 -2.571428571x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -2.571428571x + x2 = 0.7142857143 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 = 0.7142857143 + 1.653061225 Reorder the terms: 1.653061225 + -2.571428571x + x2 = 0.7142857143 + 1.653061225 Combine like terms: 0.7142857143 + 1.653061225 = 2.3673469393 1.653061225 + -2.571428571x + x2 = 2.3673469393 Factor a perfect square on the left side: (x + -1.285714286)(x + -1.285714286) = 2.3673469393 Calculate the square root of the right side: 1.538618516 Break this problem into two subproblems by setting (x + -1.285714286) equal to 1.538618516 and -1.538618516.Subproblem 1
x + -1.285714286 = 1.538618516 Simplifying x + -1.285714286 = 1.538618516 Reorder the terms: -1.285714286 + x = 1.538618516 Solving -1.285714286 + x = 1.538618516 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 = 1.538618516 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = 1.538618516 + 1.285714286 x = 1.538618516 + 1.285714286 Combine like terms: 1.538618516 + 1.285714286 = 2.824332802 x = 2.824332802 Simplifying x = 2.824332802Subproblem 2
x + -1.285714286 = -1.538618516 Simplifying x + -1.285714286 = -1.538618516 Reorder the terms: -1.285714286 + x = -1.538618516 Solving -1.285714286 + x = -1.538618516 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 = -1.538618516 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = -1.538618516 + 1.285714286 x = -1.538618516 + 1.285714286 Combine like terms: -1.538618516 + 1.285714286 = -0.25290423 x = -0.25290423 Simplifying x = -0.25290423Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.824332802, -0.25290423}
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