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Simplifying 3x2 + -2 * 81x = 25 Multiply -2 * 81 3x2 + -162x = 25 Reorder the terms: -162x + 3x2 = 25 Solving -162x + 3x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -162x + 3x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -162x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.333333333 + -54x + x2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + -54x + 8.333333333 + x2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + -54x + x2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + -54x + x2 = 0 + 8.333333333 -54x + x2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 -54x + x2 = 8.333333333 The x term is -54x. Take half its coefficient (-27). Square it (729) and add it to both sides. Add '729' to each side of the equation. -54x + 729 + x2 = 8.333333333 + 729 Reorder the terms: 729 + -54x + x2 = 8.333333333 + 729 Combine like terms: 8.333333333 + 729 = 737.333333333 729 + -54x + x2 = 737.333333333 Factor a perfect square on the left side: (x + -27)(x + -27) = 737.333333333 Calculate the square root of the right side: 27.153882473 Break this problem into two subproblems by setting (x + -27) equal to 27.153882473 and -27.153882473.Subproblem 1
x + -27 = 27.153882473 Simplifying x + -27 = 27.153882473 Reorder the terms: -27 + x = 27.153882473 Solving -27 + x = 27.153882473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x = 27.153882473 + 27 Combine like terms: -27 + 27 = 0 0 + x = 27.153882473 + 27 x = 27.153882473 + 27 Combine like terms: 27.153882473 + 27 = 54.153882473 x = 54.153882473 Simplifying x = 54.153882473Subproblem 2
x + -27 = -27.153882473 Simplifying x + -27 = -27.153882473 Reorder the terms: -27 + x = -27.153882473 Solving -27 + x = -27.153882473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x = -27.153882473 + 27 Combine like terms: -27 + 27 = 0 0 + x = -27.153882473 + 27 x = -27.153882473 + 27 Combine like terms: -27.153882473 + 27 = -0.153882473 x = -0.153882473 Simplifying x = -0.153882473Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.153882473, -0.153882473}
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