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Simplifying x2 + -72x + -89 = 0 Reorder the terms: -89 + -72x + x2 = 0 Solving -89 + -72x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + -72x + 89 + x2 = 0 + 89 Reorder the terms: -89 + 89 + -72x + x2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + -72x + x2 = 0 + 89 -72x + x2 = 0 + 89 Combine like terms: 0 + 89 = 89 -72x + x2 = 89 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 = 89 + 1296 Reorder the terms: 1296 + -72x + x2 = 89 + 1296 Combine like terms: 89 + 1296 = 1385 1296 + -72x + x2 = 1385 Factor a perfect square on the left side: (x + -36)(x + -36) = 1385 Calculate the square root of the right side: 37.215588132 Break this problem into two subproblems by setting (x + -36) equal to 37.215588132 and -37.215588132.Subproblem 1
x + -36 = 37.215588132 Simplifying x + -36 = 37.215588132 Reorder the terms: -36 + x = 37.215588132 Solving -36 + x = 37.215588132 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 = 37.215588132 + 36 Combine like terms: -36 + 36 = 0 0 + x = 37.215588132 + 36 x = 37.215588132 + 36 Combine like terms: 37.215588132 + 36 = 73.215588132 x = 73.215588132 Simplifying x = 73.215588132Subproblem 2
x + -36 = -37.215588132 Simplifying x + -36 = -37.215588132 Reorder the terms: -36 + x = -37.215588132 Solving -36 + x = -37.215588132 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 = -37.215588132 + 36 Combine like terms: -36 + 36 = 0 0 + x = -37.215588132 + 36 x = -37.215588132 + 36 Combine like terms: -37.215588132 + 36 = -1.215588132 x = -1.215588132 Simplifying x = -1.215588132Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.215588132, -1.215588132}
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