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Simplifying x2 + 41x + -45 = 0 Reorder the terms: -45 + 41x + x2 = 0 Solving -45 + 41x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 41x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 41x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 41x + x2 = 0 + 45 41x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 41x + x2 = 45 The x term is 41x. Take half its coefficient (20.5). Square it (420.25) and add it to both sides. Add '420.25' to each side of the equation. 41x + 420.25 + x2 = 45 + 420.25 Reorder the terms: 420.25 + 41x + x2 = 45 + 420.25 Combine like terms: 45 + 420.25 = 465.25 420.25 + 41x + x2 = 465.25 Factor a perfect square on the left side: (x + 20.5)(x + 20.5) = 465.25 Calculate the square root of the right side: 21.56965461 Break this problem into two subproblems by setting (x + 20.5) equal to 21.56965461 and -21.56965461.Subproblem 1
x + 20.5 = 21.56965461 Simplifying x + 20.5 = 21.56965461 Reorder the terms: 20.5 + x = 21.56965461 Solving 20.5 + x = 21.56965461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = 21.56965461 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = 21.56965461 + -20.5 x = 21.56965461 + -20.5 Combine like terms: 21.56965461 + -20.5 = 1.06965461 x = 1.06965461 Simplifying x = 1.06965461Subproblem 2
x + 20.5 = -21.56965461 Simplifying x + 20.5 = -21.56965461 Reorder the terms: 20.5 + x = -21.56965461 Solving 20.5 + x = -21.56965461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = -21.56965461 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = -21.56965461 + -20.5 x = -21.56965461 + -20.5 Combine like terms: -21.56965461 + -20.5 = -42.06965461 x = -42.06965461 Simplifying x = -42.06965461Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.06965461, -42.06965461}
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