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Simplifying 21x2 + -35x + -54 = 0 Reorder the terms: -54 + -35x + 21x2 = 0 Solving -54 + -35x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -2.571428571 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + -1.666666667x + 2.571428571 + x2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + -1.666666667x + x2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + 2.571428571 -1.666666667x + x2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 -1.666666667x + x2 = 2.571428571 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 2.571428571 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 2.571428571 + 0.6944444447 Combine like terms: 2.571428571 + 0.6944444447 = 3.2658730157 0.6944444447 + -1.666666667x + x2 = 3.2658730157 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 3.2658730157 Calculate the square root of the right side: 1.807172658 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.807172658 and -1.807172658.Subproblem 1
x + -0.8333333335 = 1.807172658 Simplifying x + -0.8333333335 = 1.807172658 Reorder the terms: -0.8333333335 + x = 1.807172658 Solving -0.8333333335 + x = 1.807172658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.807172658 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.807172658 + 0.8333333335 x = 1.807172658 + 0.8333333335 Combine like terms: 1.807172658 + 0.8333333335 = 2.6405059915 x = 2.6405059915 Simplifying x = 2.6405059915Subproblem 2
x + -0.8333333335 = -1.807172658 Simplifying x + -0.8333333335 = -1.807172658 Reorder the terms: -0.8333333335 + x = -1.807172658 Solving -0.8333333335 + x = -1.807172658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.807172658 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.807172658 + 0.8333333335 x = -1.807172658 + 0.8333333335 Combine like terms: -1.807172658 + 0.8333333335 = -0.9738393245 x = -0.9738393245 Simplifying x = -0.9738393245Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6405059915, -0.9738393245}
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