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Simplifying x2 + -43x + -340 = 0 Reorder the terms: -340 + -43x + x2 = 0 Solving -340 + -43x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '340' to each side of the equation. -340 + -43x + 340 + x2 = 0 + 340 Reorder the terms: -340 + 340 + -43x + x2 = 0 + 340 Combine like terms: -340 + 340 = 0 0 + -43x + x2 = 0 + 340 -43x + x2 = 0 + 340 Combine like terms: 0 + 340 = 340 -43x + x2 = 340 The x term is -43x. Take half its coefficient (-21.5). Square it (462.25) and add it to both sides. Add '462.25' to each side of the equation. -43x + 462.25 + x2 = 340 + 462.25 Reorder the terms: 462.25 + -43x + x2 = 340 + 462.25 Combine like terms: 340 + 462.25 = 802.25 462.25 + -43x + x2 = 802.25 Factor a perfect square on the left side: (x + -21.5)(x + -21.5) = 802.25 Calculate the square root of the right side: 28.324018077 Break this problem into two subproblems by setting (x + -21.5) equal to 28.324018077 and -28.324018077.Subproblem 1
x + -21.5 = 28.324018077 Simplifying x + -21.5 = 28.324018077 Reorder the terms: -21.5 + x = 28.324018077 Solving -21.5 + x = 28.324018077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.5' to each side of the equation. -21.5 + 21.5 + x = 28.324018077 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + x = 28.324018077 + 21.5 x = 28.324018077 + 21.5 Combine like terms: 28.324018077 + 21.5 = 49.824018077 x = 49.824018077 Simplifying x = 49.824018077Subproblem 2
x + -21.5 = -28.324018077 Simplifying x + -21.5 = -28.324018077 Reorder the terms: -21.5 + x = -28.324018077 Solving -21.5 + x = -28.324018077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.5' to each side of the equation. -21.5 + 21.5 + x = -28.324018077 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + x = -28.324018077 + 21.5 x = -28.324018077 + 21.5 Combine like terms: -28.324018077 + 21.5 = -6.824018077 x = -6.824018077 Simplifying x = -6.824018077Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.824018077, -6.824018077}
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