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Simplifying X2 + (2X + -3) = 225 Reorder the terms: X2 + (-3 + 2X) = 225 Remove parenthesis around (-3 + 2X) X2 + -3 + 2X = 225 Reorder the terms: -3 + 2X + X2 = 225 Solving -3 + 2X + X2 = 225 Solving for variable 'X'. Reorder the terms: -3 + -225 + 2X + X2 = 225 + -225 Combine like terms: -3 + -225 = -228 -228 + 2X + X2 = 225 + -225 Combine like terms: 225 + -225 = 0 -228 + 2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '228' to each side of the equation. -228 + 2X + 228 + X2 = 0 + 228 Reorder the terms: -228 + 228 + 2X + X2 = 0 + 228 Combine like terms: -228 + 228 = 0 0 + 2X + X2 = 0 + 228 2X + X2 = 0 + 228 Combine like terms: 0 + 228 = 228 2X + X2 = 228 The X term is 2X. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2X + 1 + X2 = 228 + 1 Reorder the terms: 1 + 2X + X2 = 228 + 1 Combine like terms: 228 + 1 = 229 1 + 2X + X2 = 229 Factor a perfect square on the left side: (X + 1)(X + 1) = 229 Calculate the square root of the right side: 15.13274595 Break this problem into two subproblems by setting (X + 1) equal to 15.13274595 and -15.13274595.Subproblem 1
X + 1 = 15.13274595 Simplifying X + 1 = 15.13274595 Reorder the terms: 1 + X = 15.13274595 Solving 1 + X = 15.13274595 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = 15.13274595 + -1 Combine like terms: 1 + -1 = 0 0 + X = 15.13274595 + -1 X = 15.13274595 + -1 Combine like terms: 15.13274595 + -1 = 14.13274595 X = 14.13274595 Simplifying X = 14.13274595Subproblem 2
X + 1 = -15.13274595 Simplifying X + 1 = -15.13274595 Reorder the terms: 1 + X = -15.13274595 Solving 1 + X = -15.13274595 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = -15.13274595 + -1 Combine like terms: 1 + -1 = 0 0 + X = -15.13274595 + -1 X = -15.13274595 + -1 Combine like terms: -15.13274595 + -1 = -16.13274595 X = -16.13274595 Simplifying X = -16.13274595Solution
The solution to the problem is based on the solutions from the subproblems. X = {14.13274595, -16.13274595}
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