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Simplifying x2 = 72x + 9 Reorder the terms: x2 = 9 + 72x Solving x2 = 9 + 72x Solving for variable 'x'. Reorder the terms: -9 + -72x + x2 = 9 + 72x + -9 + -72x Reorder the terms: -9 + -72x + x2 = 9 + -9 + 72x + -72x Combine like terms: 9 + -9 = 0 -9 + -72x + x2 = 0 + 72x + -72x -9 + -72x + x2 = 72x + -72x Combine like terms: 72x + -72x = 0 -9 + -72x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -72x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -72x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -72x + x2 = 0 + 9 -72x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -72x + x2 = 9 The x term is -72x. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x + 1296 + x2 = 9 + 1296 Reorder the terms: 1296 + -72x + x2 = 9 + 1296 Combine like terms: 9 + 1296 = 1305 1296 + -72x + x2 = 1305 Factor a perfect square on the left side: (x + -36)(x + -36) = 1305 Calculate the square root of the right side: 36.124783736 Break this problem into two subproblems by setting (x + -36) equal to 36.124783736 and -36.124783736.Subproblem 1
x + -36 = 36.124783736 Simplifying x + -36 = 36.124783736 Reorder the terms: -36 + x = 36.124783736 Solving -36 + x = 36.124783736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 36.124783736 + 36 Combine like terms: -36 + 36 = 0 0 + x = 36.124783736 + 36 x = 36.124783736 + 36 Combine like terms: 36.124783736 + 36 = 72.124783736 x = 72.124783736 Simplifying x = 72.124783736Subproblem 2
x + -36 = -36.124783736 Simplifying x + -36 = -36.124783736 Reorder the terms: -36 + x = -36.124783736 Solving -36 + x = -36.124783736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -36.124783736 + 36 Combine like terms: -36 + 36 = 0 0 + x = -36.124783736 + 36 x = -36.124783736 + 36 Combine like terms: -36.124783736 + 36 = -0.124783736 x = -0.124783736 Simplifying x = -0.124783736Solution
The solution to the problem is based on the solutions from the subproblems. x = {72.124783736, -0.124783736}
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