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Simplifying X2 + 10X + -135 = 0 Reorder the terms: -135 + 10X + X2 = 0 Solving -135 + 10X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '135' to each side of the equation. -135 + 10X + 135 + X2 = 0 + 135 Reorder the terms: -135 + 135 + 10X + X2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + 10X + X2 = 0 + 135 10X + X2 = 0 + 135 Combine like terms: 0 + 135 = 135 10X + X2 = 135 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 = 135 + 25 Reorder the terms: 25 + 10X + X2 = 135 + 25 Combine like terms: 135 + 25 = 160 25 + 10X + X2 = 160 Factor a perfect square on the left side: (X + 5)(X + 5) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (X + 5) equal to 12.649110641 and -12.649110641.Subproblem 1
X + 5 = 12.649110641 Simplifying X + 5 = 12.649110641 Reorder the terms: 5 + X = 12.649110641 Solving 5 + X = 12.649110641 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 = 12.649110641 + -5 Combine like terms: 5 + -5 = 0 0 + X = 12.649110641 + -5 X = 12.649110641 + -5 Combine like terms: 12.649110641 + -5 = 7.649110641 X = 7.649110641 Simplifying X = 7.649110641Subproblem 2
X + 5 = -12.649110641 Simplifying X + 5 = -12.649110641 Reorder the terms: 5 + X = -12.649110641 Solving 5 + X = -12.649110641 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 = -12.649110641 + -5 Combine like terms: 5 + -5 = 0 0 + X = -12.649110641 + -5 X = -12.649110641 + -5 Combine like terms: -12.649110641 + -5 = -17.649110641 X = -17.649110641 Simplifying X = -17.649110641Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.649110641, -17.649110641}
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