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Simplifying x2 + 105x + -140 = 0 Reorder the terms: -140 + 105x + x2 = 0 Solving -140 + 105x + 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 + 105x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 105x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 105x + x2 = 0 + 140 105x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 105x + x2 = 140 The x term is 105x. Take half its coefficient (52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. 105x + 2756.25 + x2 = 140 + 2756.25 Reorder the terms: 2756.25 + 105x + x2 = 140 + 2756.25 Combine like terms: 140 + 2756.25 = 2896.25 2756.25 + 105x + x2 = 2896.25 Factor a perfect square on the left side: (x + 52.5)(x + 52.5) = 2896.25 Calculate the square root of the right side: 53.816818932 Break this problem into two subproblems by setting (x + 52.5) equal to 53.816818932 and -53.816818932.Subproblem 1
x + 52.5 = 53.816818932 Simplifying x + 52.5 = 53.816818932 Reorder the terms: 52.5 + x = 53.816818932 Solving 52.5 + x = 53.816818932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + x = 53.816818932 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + x = 53.816818932 + -52.5 x = 53.816818932 + -52.5 Combine like terms: 53.816818932 + -52.5 = 1.316818932 x = 1.316818932 Simplifying x = 1.316818932Subproblem 2
x + 52.5 = -53.816818932 Simplifying x + 52.5 = -53.816818932 Reorder the terms: 52.5 + x = -53.816818932 Solving 52.5 + x = -53.816818932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + x = -53.816818932 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + x = -53.816818932 + -52.5 x = -53.816818932 + -52.5 Combine like terms: -53.816818932 + -52.5 = -106.316818932 x = -106.316818932 Simplifying x = -106.316818932Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.316818932, -106.316818932}
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