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Simplifying 4x2 + 45x + 100 = 0 Reorder the terms: 100 + 45x + 4x2 = 0 Solving 100 + 45x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 25 + 11.25x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + 11.25x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + 11.25x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 11.25x + x2 = 0 + -25 11.25x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 11.25x + x2 = -25 The x term is 11.25x. Take half its coefficient (5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. 11.25x + 31.640625 + x2 = -25 + 31.640625 Reorder the terms: 31.640625 + 11.25x + x2 = -25 + 31.640625 Combine like terms: -25 + 31.640625 = 6.640625 31.640625 + 11.25x + x2 = 6.640625 Factor a perfect square on the left side: (x + 5.625)(x + 5.625) = 6.640625 Calculate the square root of the right side: 2.576941016 Break this problem into two subproblems by setting (x + 5.625) equal to 2.576941016 and -2.576941016.Subproblem 1
x + 5.625 = 2.576941016 Simplifying x + 5.625 = 2.576941016 Reorder the terms: 5.625 + x = 2.576941016 Solving 5.625 + x = 2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.625' to each side of the equation. 5.625 + -5.625 + x = 2.576941016 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + x = 2.576941016 + -5.625 x = 2.576941016 + -5.625 Combine like terms: 2.576941016 + -5.625 = -3.048058984 x = -3.048058984 Simplifying x = -3.048058984Subproblem 2
x + 5.625 = -2.576941016 Simplifying x + 5.625 = -2.576941016 Reorder the terms: 5.625 + x = -2.576941016 Solving 5.625 + x = -2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.625' to each side of the equation. 5.625 + -5.625 + x = -2.576941016 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + x = -2.576941016 + -5.625 x = -2.576941016 + -5.625 Combine like terms: -2.576941016 + -5.625 = -8.201941016 x = -8.201941016 Simplifying x = -8.201941016Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.048058984, -8.201941016}
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