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Simplifying x2 + -42x + -185 = 0 Reorder the terms: -185 + -42x + x2 = 0 Solving -185 + -42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '185' to each side of the equation. -185 + -42x + 185 + x2 = 0 + 185 Reorder the terms: -185 + 185 + -42x + x2 = 0 + 185 Combine like terms: -185 + 185 = 0 0 + -42x + x2 = 0 + 185 -42x + x2 = 0 + 185 Combine like terms: 0 + 185 = 185 -42x + x2 = 185 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = 185 + 441 Reorder the terms: 441 + -42x + x2 = 185 + 441 Combine like terms: 185 + 441 = 626 441 + -42x + x2 = 626 Factor a perfect square on the left side: (x + -21)(x + -21) = 626 Calculate the square root of the right side: 25.019992006 Break this problem into two subproblems by setting (x + -21) equal to 25.019992006 and -25.019992006.Subproblem 1
x + -21 = 25.019992006 Simplifying x + -21 = 25.019992006 Reorder the terms: -21 + x = 25.019992006 Solving -21 + x = 25.019992006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 25.019992006 + 21 Combine like terms: -21 + 21 = 0 0 + x = 25.019992006 + 21 x = 25.019992006 + 21 Combine like terms: 25.019992006 + 21 = 46.019992006 x = 46.019992006 Simplifying x = 46.019992006Subproblem 2
x + -21 = -25.019992006 Simplifying x + -21 = -25.019992006 Reorder the terms: -21 + x = -25.019992006 Solving -21 + x = -25.019992006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -25.019992006 + 21 Combine like terms: -21 + 21 = 0 0 + x = -25.019992006 + 21 x = -25.019992006 + 21 Combine like terms: -25.019992006 + 21 = -4.019992006 x = -4.019992006 Simplifying x = -4.019992006Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.019992006, -4.019992006}
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