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Simplifying 0 = 4x2 + -34x + 5 Reorder the terms: 0 = 5 + -34x + 4x2 Solving 0 = 5 + -34x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + 34x + -4x2 = 5 + -34x + 4x2 + -5 + 34x + -4x2 Reorder the terms: -5 + 34x + -4x2 = 5 + -5 + -34x + 34x + 4x2 + -4x2 Combine like terms: 5 + -5 = 0 -5 + 34x + -4x2 = 0 + -34x + 34x + 4x2 + -4x2 -5 + 34x + -4x2 = -34x + 34x + 4x2 + -4x2 Combine like terms: -34x + 34x = 0 -5 + 34x + -4x2 = 0 + 4x2 + -4x2 -5 + 34x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -5 + 34x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.25 + -8.5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -8.5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -8.5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -8.5x + x2 = 0 + -1.25 -8.5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -8.5x + x2 = -1.25 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = -1.25 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -1.25 + 18.0625 Combine like terms: -1.25 + 18.0625 = 16.8125 18.0625 + -8.5x + x2 = 16.8125 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 16.8125 Calculate the square root of the right side: 4.100304867 Break this problem into two subproblems by setting (x + -4.25) equal to 4.100304867 and -4.100304867.Subproblem 1
x + -4.25 = 4.100304867 Simplifying x + -4.25 = 4.100304867 Reorder the terms: -4.25 + x = 4.100304867 Solving -4.25 + x = 4.100304867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 4.100304867 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.100304867 + 4.25 x = 4.100304867 + 4.25 Combine like terms: 4.100304867 + 4.25 = 8.350304867 x = 8.350304867 Simplifying x = 8.350304867Subproblem 2
x + -4.25 = -4.100304867 Simplifying x + -4.25 = -4.100304867 Reorder the terms: -4.25 + x = -4.100304867 Solving -4.25 + x = -4.100304867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -4.100304867 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.100304867 + 4.25 x = -4.100304867 + 4.25 Combine like terms: -4.100304867 + 4.25 = 0.149695133 x = 0.149695133 Simplifying x = 0.149695133Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.350304867, 0.149695133}
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