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Simplifying 4x2 + 5x + -83 = 0 Reorder the terms: -83 + 5x + 4x2 = 0 Solving -83 + 5x + 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'. -20.75 + 1.25x + x2 = 0 Move the constant term to the right: Add '20.75' to each side of the equation. -20.75 + 1.25x + 20.75 + x2 = 0 + 20.75 Reorder the terms: -20.75 + 20.75 + 1.25x + x2 = 0 + 20.75 Combine like terms: -20.75 + 20.75 = 0.00 0.00 + 1.25x + x2 = 0 + 20.75 1.25x + x2 = 0 + 20.75 Combine like terms: 0 + 20.75 = 20.75 1.25x + x2 = 20.75 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 20.75 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 20.75 + 0.390625 Combine like terms: 20.75 + 0.390625 = 21.140625 0.390625 + 1.25x + x2 = 21.140625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 21.140625 Calculate the square root of the right side: 4.597893539 Break this problem into two subproblems by setting (x + 0.625) equal to 4.597893539 and -4.597893539.Subproblem 1
x + 0.625 = 4.597893539 Simplifying x + 0.625 = 4.597893539 Reorder the terms: 0.625 + x = 4.597893539 Solving 0.625 + x = 4.597893539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 4.597893539 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 4.597893539 + -0.625 x = 4.597893539 + -0.625 Combine like terms: 4.597893539 + -0.625 = 3.972893539 x = 3.972893539 Simplifying x = 3.972893539Subproblem 2
x + 0.625 = -4.597893539 Simplifying x + 0.625 = -4.597893539 Reorder the terms: 0.625 + x = -4.597893539 Solving 0.625 + x = -4.597893539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -4.597893539 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -4.597893539 + -0.625 x = -4.597893539 + -0.625 Combine like terms: -4.597893539 + -0.625 = -5.222893539 x = -5.222893539 Simplifying x = -5.222893539Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.972893539, -5.222893539}
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