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Simplifying x2 + -18x = 4 Reorder the terms: -18x + x2 = 4 Solving -18x + x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -18x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -18x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -18x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -18x + x2 = 0 + 4 -18x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -18x + x2 = 4 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 4 + 81 Reorder the terms: 81 + -18x + x2 = 4 + 81 Combine like terms: 4 + 81 = 85 81 + -18x + x2 = 85 Factor a perfect square on the left side: (x + -9)(x + -9) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + -9) equal to 9.219544457 and -9.219544457.Subproblem 1
x + -9 = 9.219544457 Simplifying x + -9 = 9.219544457 Reorder the terms: -9 + x = 9.219544457 Solving -9 + x = 9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 9.219544457 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.219544457 + 9 x = 9.219544457 + 9 Combine like terms: 9.219544457 + 9 = 18.219544457 x = 18.219544457 Simplifying x = 18.219544457Subproblem 2
x + -9 = -9.219544457 Simplifying x + -9 = -9.219544457 Reorder the terms: -9 + x = -9.219544457 Solving -9 + x = -9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -9.219544457 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.219544457 + 9 x = -9.219544457 + 9 Combine like terms: -9.219544457 + 9 = -0.219544457 x = -0.219544457 Simplifying x = -0.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.219544457, -0.219544457}
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