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Simplifying x2 + -4x + -103 = -4 Reorder the terms: -103 + -4x + x2 = -4 Solving -103 + -4x + x2 = -4 Solving for variable 'x'. Reorder the terms: -103 + 4 + -4x + x2 = -4 + 4 Combine like terms: -103 + 4 = -99 -99 + -4x + x2 = -4 + 4 Combine like terms: -4 + 4 = 0 -99 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -4x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -4x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -4x + x2 = 0 + 99 -4x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -4x + x2 = 99 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 = 99 + 4 Reorder the terms: 4 + -4x + x2 = 99 + 4 Combine like terms: 99 + 4 = 103 4 + -4x + x2 = 103 Factor a perfect square on the left side: (x + -2)(x + -2) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (x + -2) equal to 10.148891565 and -10.148891565.Subproblem 1
x + -2 = 10.148891565 Simplifying x + -2 = 10.148891565 Reorder the terms: -2 + x = 10.148891565 Solving -2 + x = 10.148891565 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 = 10.148891565 + 2 Combine like terms: -2 + 2 = 0 0 + x = 10.148891565 + 2 x = 10.148891565 + 2 Combine like terms: 10.148891565 + 2 = 12.148891565 x = 12.148891565 Simplifying x = 12.148891565Subproblem 2
x + -2 = -10.148891565 Simplifying x + -2 = -10.148891565 Reorder the terms: -2 + x = -10.148891565 Solving -2 + x = -10.148891565 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 = -10.148891565 + 2 Combine like terms: -2 + 2 = 0 0 + x = -10.148891565 + 2 x = -10.148891565 + 2 Combine like terms: -10.148891565 + 2 = -8.148891565 x = -8.148891565 Simplifying x = -8.148891565Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.148891565, -8.148891565}
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