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Simplifying x2 + 20x + -100 = 4 Reorder the terms: -100 + 20x + x2 = 4 Solving -100 + 20x + x2 = 4 Solving for variable 'x'. Reorder the terms: -100 + -4 + 20x + x2 = 4 + -4 Combine like terms: -100 + -4 = -104 -104 + 20x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -104 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + 20x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + 20x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + 20x + x2 = 0 + 104 20x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 20x + x2 = 104 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 104 + 100 Reorder the terms: 100 + 20x + x2 = 104 + 100 Combine like terms: 104 + 100 = 204 100 + 20x + x2 = 204 Factor a perfect square on the left side: (x + 10)(x + 10) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (x + 10) equal to 14.282856857 and -14.282856857.Subproblem 1
x + 10 = 14.282856857 Simplifying x + 10 = 14.282856857 Reorder the terms: 10 + x = 14.282856857 Solving 10 + x = 14.282856857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 14.282856857 + -10 Combine like terms: 10 + -10 = 0 0 + x = 14.282856857 + -10 x = 14.282856857 + -10 Combine like terms: 14.282856857 + -10 = 4.282856857 x = 4.282856857 Simplifying x = 4.282856857Subproblem 2
x + 10 = -14.282856857 Simplifying x + 10 = -14.282856857 Reorder the terms: 10 + x = -14.282856857 Solving 10 + x = -14.282856857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -14.282856857 + -10 Combine like terms: 10 + -10 = 0 0 + x = -14.282856857 + -10 x = -14.282856857 + -10 Combine like terms: -14.282856857 + -10 = -24.282856857 x = -24.282856857 Simplifying x = -24.282856857Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.282856857, -24.282856857}
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