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Simplifying x2 + -6x2 + -81x + 486 = 0 Reorder the terms: 486 + -81x + x2 + -6x2 = 0 Combine like terms: x2 + -6x2 = -5x2 486 + -81x + -5x2 = 0 Solving 486 + -81x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -97.2 + 16.2x + x2 = 0 Move the constant term to the right: Add '97.2' to each side of the equation. -97.2 + 16.2x + 97.2 + x2 = 0 + 97.2 Reorder the terms: -97.2 + 97.2 + 16.2x + x2 = 0 + 97.2 Combine like terms: -97.2 + 97.2 = 0.0 0.0 + 16.2x + x2 = 0 + 97.2 16.2x + x2 = 0 + 97.2 Combine like terms: 0 + 97.2 = 97.2 16.2x + x2 = 97.2 The x term is 16.2x. Take half its coefficient (8.1). Square it (65.61) and add it to both sides. Add '65.61' to each side of the equation. 16.2x + 65.61 + x2 = 97.2 + 65.61 Reorder the terms: 65.61 + 16.2x + x2 = 97.2 + 65.61 Combine like terms: 97.2 + 65.61 = 162.81 65.61 + 16.2x + x2 = 162.81 Factor a perfect square on the left side: (x + 8.1)(x + 8.1) = 162.81 Calculate the square root of the right side: 12.759702191 Break this problem into two subproblems by setting (x + 8.1) equal to 12.759702191 and -12.759702191.Subproblem 1
x + 8.1 = 12.759702191 Simplifying x + 8.1 = 12.759702191 Reorder the terms: 8.1 + x = 12.759702191 Solving 8.1 + x = 12.759702191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.1' to each side of the equation. 8.1 + -8.1 + x = 12.759702191 + -8.1 Combine like terms: 8.1 + -8.1 = 0.0 0.0 + x = 12.759702191 + -8.1 x = 12.759702191 + -8.1 Combine like terms: 12.759702191 + -8.1 = 4.659702191 x = 4.659702191 Simplifying x = 4.659702191Subproblem 2
x + 8.1 = -12.759702191 Simplifying x + 8.1 = -12.759702191 Reorder the terms: 8.1 + x = -12.759702191 Solving 8.1 + x = -12.759702191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.1' to each side of the equation. 8.1 + -8.1 + x = -12.759702191 + -8.1 Combine like terms: 8.1 + -8.1 = 0.0 0.0 + x = -12.759702191 + -8.1 x = -12.759702191 + -8.1 Combine like terms: -12.759702191 + -8.1 = -20.859702191 x = -20.859702191 Simplifying x = -20.859702191Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.659702191, -20.859702191}
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