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Simplifying x2 + -10x + -140 = 0 Reorder the terms: -140 + -10x + x2 = 0 Solving -140 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + -10x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + -10x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -10x + x2 = 0 + 140 -10x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 -10x + x2 = 140 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 140 + 25 Reorder the terms: 25 + -10x + x2 = 140 + 25 Combine like terms: 140 + 25 = 165 25 + -10x + x2 = 165 Factor a perfect square on the left side: (x + -5)(x + -5) = 165 Calculate the square root of the right side: 12.845232579 Break this problem into two subproblems by setting (x + -5) equal to 12.845232579 and -12.845232579.Subproblem 1
x + -5 = 12.845232579 Simplifying x + -5 = 12.845232579 Reorder the terms: -5 + x = 12.845232579 Solving -5 + x = 12.845232579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 12.845232579 + 5 Combine like terms: -5 + 5 = 0 0 + x = 12.845232579 + 5 x = 12.845232579 + 5 Combine like terms: 12.845232579 + 5 = 17.845232579 x = 17.845232579 Simplifying x = 17.845232579Subproblem 2
x + -5 = -12.845232579 Simplifying x + -5 = -12.845232579 Reorder the terms: -5 + x = -12.845232579 Solving -5 + x = -12.845232579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -12.845232579 + 5 Combine like terms: -5 + 5 = 0 0 + x = -12.845232579 + 5 x = -12.845232579 + 5 Combine like terms: -12.845232579 + 5 = -7.845232579 x = -7.845232579 Simplifying x = -7.845232579Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.845232579, -7.845232579}
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