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Simplifying x2 + -74x + -12 = 0 Reorder the terms: -12 + -74x + x2 = 0 Solving -12 + -74x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -74x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -74x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -74x + x2 = 0 + 12 -74x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -74x + x2 = 12 The x term is -74x. Take half its coefficient (-37). Square it (1369) and add it to both sides. Add '1369' to each side of the equation. -74x + 1369 + x2 = 12 + 1369 Reorder the terms: 1369 + -74x + x2 = 12 + 1369 Combine like terms: 12 + 1369 = 1381 1369 + -74x + x2 = 1381 Factor a perfect square on the left side: (x + -37)(x + -37) = 1381 Calculate the square root of the right side: 37.161808352 Break this problem into two subproblems by setting (x + -37) equal to 37.161808352 and -37.161808352.Subproblem 1
x + -37 = 37.161808352 Simplifying x + -37 = 37.161808352 Reorder the terms: -37 + x = 37.161808352 Solving -37 + x = 37.161808352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + x = 37.161808352 + 37 Combine like terms: -37 + 37 = 0 0 + x = 37.161808352 + 37 x = 37.161808352 + 37 Combine like terms: 37.161808352 + 37 = 74.161808352 x = 74.161808352 Simplifying x = 74.161808352Subproblem 2
x + -37 = -37.161808352 Simplifying x + -37 = -37.161808352 Reorder the terms: -37 + x = -37.161808352 Solving -37 + x = -37.161808352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + x = -37.161808352 + 37 Combine like terms: -37 + 37 = 0 0 + x = -37.161808352 + 37 x = -37.161808352 + 37 Combine like terms: -37.161808352 + 37 = -0.161808352 x = -0.161808352 Simplifying x = -0.161808352Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.161808352, -0.161808352}
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