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Simplifying 5x2 + -10x + -81 = 0 Reorder the terms: -81 + -10x + 5x2 = 0 Solving -81 + -10x + 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'. -16.2 + -2x + x2 = 0 Move the constant term to the right: Add '16.2' to each side of the equation. -16.2 + -2x + 16.2 + x2 = 0 + 16.2 Reorder the terms: -16.2 + 16.2 + -2x + x2 = 0 + 16.2 Combine like terms: -16.2 + 16.2 = 0.0 0.0 + -2x + x2 = 0 + 16.2 -2x + x2 = 0 + 16.2 Combine like terms: 0 + 16.2 = 16.2 -2x + x2 = 16.2 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 16.2 + 1 Reorder the terms: 1 + -2x + x2 = 16.2 + 1 Combine like terms: 16.2 + 1 = 17.2 1 + -2x + x2 = 17.2 Factor a perfect square on the left side: (x + -1)(x + -1) = 17.2 Calculate the square root of the right side: 4.147288271 Break this problem into two subproblems by setting (x + -1) equal to 4.147288271 and -4.147288271.Subproblem 1
x + -1 = 4.147288271 Simplifying x + -1 = 4.147288271 Reorder the terms: -1 + x = 4.147288271 Solving -1 + x = 4.147288271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.147288271 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.147288271 + 1 x = 4.147288271 + 1 Combine like terms: 4.147288271 + 1 = 5.147288271 x = 5.147288271 Simplifying x = 5.147288271Subproblem 2
x + -1 = -4.147288271 Simplifying x + -1 = -4.147288271 Reorder the terms: -1 + x = -4.147288271 Solving -1 + x = -4.147288271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.147288271 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.147288271 + 1 x = -4.147288271 + 1 Combine like terms: -4.147288271 + 1 = -3.147288271 x = -3.147288271 Simplifying x = -3.147288271Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.147288271, -3.147288271}
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