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Simplifying x(x + -4) = 81 Reorder the terms: x(-4 + x) = 81 (-4 * x + x * x) = 81 (-4x + x2) = 81 Solving -4x + x2 = 81 Solving for variable 'x'. Reorder the terms: -81 + -4x + x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -4x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + -4x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -4x + x2 = 0 + 81 -4x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 -4x + x2 = 81 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 81 + 4 Reorder the terms: 4 + -4x + x2 = 81 + 4 Combine like terms: 81 + 4 = 85 4 + -4x + x2 = 85 Factor a perfect square on the left side: (x + -2)(x + -2) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + -2) equal to 9.219544457 and -9.219544457.Subproblem 1
x + -2 = 9.219544457 Simplifying x + -2 = 9.219544457 Reorder the terms: -2 + x = 9.219544457 Solving -2 + x = 9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 9.219544457 + 2 Combine like terms: -2 + 2 = 0 0 + x = 9.219544457 + 2 x = 9.219544457 + 2 Combine like terms: 9.219544457 + 2 = 11.219544457 x = 11.219544457 Simplifying x = 11.219544457Subproblem 2
x + -2 = -9.219544457 Simplifying x + -2 = -9.219544457 Reorder the terms: -2 + x = -9.219544457 Solving -2 + x = -9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -9.219544457 + 2 Combine like terms: -2 + 2 = 0 0 + x = -9.219544457 + 2 x = -9.219544457 + 2 Combine like terms: -9.219544457 + 2 = -7.219544457 x = -7.219544457 Simplifying x = -7.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.219544457, -7.219544457}
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