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Simplifying 18x2 + -21x + -7 = 0 Reorder the terms: -7 + -21x + 18x2 = 0 Solving -7 + -21x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.3888888889 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '0.3888888889' to each side of the equation. -0.3888888889 + -1.166666667x + 0.3888888889 + x2 = 0 + 0.3888888889 Reorder the terms: -0.3888888889 + 0.3888888889 + -1.166666667x + x2 = 0 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + -1.166666667x + x2 = 0 + 0.3888888889 -1.166666667x + x2 = 0 + 0.3888888889 Combine like terms: 0 + 0.3888888889 = 0.3888888889 -1.166666667x + x2 = 0.3888888889 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = 0.3888888889 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 0.3888888889 + 0.3402777780 Combine like terms: 0.3888888889 + 0.3402777780 = 0.7291666669 0.3402777780 + -1.166666667x + x2 = 0.7291666669 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 0.7291666669 Calculate the square root of the right side: 0.853912564 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 0.853912564 and -0.853912564.Subproblem 1
x + -0.5833333335 = 0.853912564 Simplifying x + -0.5833333335 = 0.853912564 Reorder the terms: -0.5833333335 + x = 0.853912564 Solving -0.5833333335 + x = 0.853912564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 0.853912564 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 0.853912564 + 0.5833333335 x = 0.853912564 + 0.5833333335 Combine like terms: 0.853912564 + 0.5833333335 = 1.4372458975 x = 1.4372458975 Simplifying x = 1.4372458975Subproblem 2
x + -0.5833333335 = -0.853912564 Simplifying x + -0.5833333335 = -0.853912564 Reorder the terms: -0.5833333335 + x = -0.853912564 Solving -0.5833333335 + x = -0.853912564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -0.853912564 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -0.853912564 + 0.5833333335 x = -0.853912564 + 0.5833333335 Combine like terms: -0.853912564 + 0.5833333335 = -0.2705792305 x = -0.2705792305 Simplifying x = -0.2705792305Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4372458975, -0.2705792305}
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