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Simplifying x2 + 4x + 5 = 100 Reorder the terms: 5 + 4x + x2 = 100 Solving 5 + 4x + x2 = 100 Solving for variable 'x'. Reorder the terms: 5 + -100 + 4x + x2 = 100 + -100 Combine like terms: 5 + -100 = -95 -95 + 4x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -95 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + 4x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + 4x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + 4x + x2 = 0 + 95 4x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 4x + x2 = 95 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 = 95 + 4 Reorder the terms: 4 + 4x + x2 = 95 + 4 Combine like terms: 95 + 4 = 99 4 + 4x + x2 = 99 Factor a perfect square on the left side: (x + 2)(x + 2) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + 2) equal to 9.949874371 and -9.949874371.Subproblem 1
x + 2 = 9.949874371 Simplifying x + 2 = 9.949874371 Reorder the terms: 2 + x = 9.949874371 Solving 2 + x = 9.949874371 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 = 9.949874371 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.949874371 + -2 x = 9.949874371 + -2 Combine like terms: 9.949874371 + -2 = 7.949874371 x = 7.949874371 Simplifying x = 7.949874371Subproblem 2
x + 2 = -9.949874371 Simplifying x + 2 = -9.949874371 Reorder the terms: 2 + x = -9.949874371 Solving 2 + x = -9.949874371 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 = -9.949874371 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.949874371 + -2 x = -9.949874371 + -2 Combine like terms: -9.949874371 + -2 = -11.949874371 x = -11.949874371 Simplifying x = -11.949874371Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.949874371, -11.949874371}
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