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Simplifying 4x2 + 43x + 89 = 0 Reorder the terms: 89 + 43x + 4x2 = 0 Solving 89 + 43x + 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'. 22.25 + 10.75x + x2 = 0 Move the constant term to the right: Add '-22.25' to each side of the equation. 22.25 + 10.75x + -22.25 + x2 = 0 + -22.25 Reorder the terms: 22.25 + -22.25 + 10.75x + x2 = 0 + -22.25 Combine like terms: 22.25 + -22.25 = 0.00 0.00 + 10.75x + x2 = 0 + -22.25 10.75x + x2 = 0 + -22.25 Combine like terms: 0 + -22.25 = -22.25 10.75x + x2 = -22.25 The x term is 10.75x. Take half its coefficient (5.375). Square it (28.890625) and add it to both sides. Add '28.890625' to each side of the equation. 10.75x + 28.890625 + x2 = -22.25 + 28.890625 Reorder the terms: 28.890625 + 10.75x + x2 = -22.25 + 28.890625 Combine like terms: -22.25 + 28.890625 = 6.640625 28.890625 + 10.75x + x2 = 6.640625 Factor a perfect square on the left side: (x + 5.375)(x + 5.375) = 6.640625 Calculate the square root of the right side: 2.576941016 Break this problem into two subproblems by setting (x + 5.375) equal to 2.576941016 and -2.576941016.Subproblem 1
x + 5.375 = 2.576941016 Simplifying x + 5.375 = 2.576941016 Reorder the terms: 5.375 + x = 2.576941016 Solving 5.375 + x = 2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.375' to each side of the equation. 5.375 + -5.375 + x = 2.576941016 + -5.375 Combine like terms: 5.375 + -5.375 = 0.000 0.000 + x = 2.576941016 + -5.375 x = 2.576941016 + -5.375 Combine like terms: 2.576941016 + -5.375 = -2.798058984 x = -2.798058984 Simplifying x = -2.798058984Subproblem 2
x + 5.375 = -2.576941016 Simplifying x + 5.375 = -2.576941016 Reorder the terms: 5.375 + x = -2.576941016 Solving 5.375 + x = -2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.375' to each side of the equation. 5.375 + -5.375 + x = -2.576941016 + -5.375 Combine like terms: 5.375 + -5.375 = 0.000 0.000 + x = -2.576941016 + -5.375 x = -2.576941016 + -5.375 Combine like terms: -2.576941016 + -5.375 = -7.951941016 x = -7.951941016 Simplifying x = -7.951941016Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.798058984, -7.951941016}
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