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Simplifying x2 + 4.25x + -16 = 100 Reorder the terms: -16 + 4.25x + x2 = 100 Solving -16 + 4.25x + x2 = 100 Solving for variable 'x'. Reorder the terms: -16 + -100 + 4.25x + x2 = 100 + -100 Combine like terms: -16 + -100 = -116 -116 + 4.25x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -116 + 4.25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '116' to each side of the equation. -116 + 4.25x + 116 + x2 = 0 + 116 Reorder the terms: -116 + 116 + 4.25x + x2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + 4.25x + x2 = 0 + 116 4.25x + x2 = 0 + 116 Combine like terms: 0 + 116 = 116 4.25x + x2 = 116 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 116 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 116 + 4.515625 Combine like terms: 116 + 4.515625 = 120.515625 4.515625 + 4.25x + x2 = 120.515625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 120.515625 Calculate the square root of the right side: 10.977960876 Break this problem into two subproblems by setting (x + 2.125) equal to 10.977960876 and -10.977960876.Subproblem 1
x + 2.125 = 10.977960876 Simplifying x + 2.125 = 10.977960876 Reorder the terms: 2.125 + x = 10.977960876 Solving 2.125 + x = 10.977960876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 10.977960876 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 10.977960876 + -2.125 x = 10.977960876 + -2.125 Combine like terms: 10.977960876 + -2.125 = 8.852960876 x = 8.852960876 Simplifying x = 8.852960876Subproblem 2
x + 2.125 = -10.977960876 Simplifying x + 2.125 = -10.977960876 Reorder the terms: 2.125 + x = -10.977960876 Solving 2.125 + x = -10.977960876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -10.977960876 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -10.977960876 + -2.125 x = -10.977960876 + -2.125 Combine like terms: -10.977960876 + -2.125 = -13.102960876 x = -13.102960876 Simplifying x = -13.102960876Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.852960876, -13.102960876}
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