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Simplifying x2 + 4x + -198 = 100 Reorder the terms: -198 + 4x + x2 = 100 Solving -198 + 4x + x2 = 100 Solving for variable 'x'. Reorder the terms: -198 + -100 + 4x + x2 = 100 + -100 Combine like terms: -198 + -100 = -298 -298 + 4x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -298 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '298' to each side of the equation. -298 + 4x + 298 + x2 = 0 + 298 Reorder the terms: -298 + 298 + 4x + x2 = 0 + 298 Combine like terms: -298 + 298 = 0 0 + 4x + x2 = 0 + 298 4x + x2 = 0 + 298 Combine like terms: 0 + 298 = 298 4x + x2 = 298 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 298 + 4 Reorder the terms: 4 + 4x + x2 = 298 + 4 Combine like terms: 298 + 4 = 302 4 + 4x + x2 = 302 Factor a perfect square on the left side: (x + 2)(x + 2) = 302 Calculate the square root of the right side: 17.378147197 Break this problem into two subproblems by setting (x + 2) equal to 17.378147197 and -17.378147197.Subproblem 1
x + 2 = 17.378147197 Simplifying x + 2 = 17.378147197 Reorder the terms: 2 + x = 17.378147197 Solving 2 + x = 17.378147197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 17.378147197 + -2 Combine like terms: 2 + -2 = 0 0 + x = 17.378147197 + -2 x = 17.378147197 + -2 Combine like terms: 17.378147197 + -2 = 15.378147197 x = 15.378147197 Simplifying x = 15.378147197Subproblem 2
x + 2 = -17.378147197 Simplifying x + 2 = -17.378147197 Reorder the terms: 2 + x = -17.378147197 Solving 2 + x = -17.378147197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -17.378147197 + -2 Combine like terms: 2 + -2 = 0 0 + x = -17.378147197 + -2 x = -17.378147197 + -2 Combine like terms: -17.378147197 + -2 = -19.378147197 x = -19.378147197 Simplifying x = -19.378147197Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.378147197, -19.378147197}
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