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Simplifying 4x2 + -49x + 134 = 0 Reorder the terms: 134 + -49x + 4x2 = 0 Solving 134 + -49x + 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'. 33.5 + -12.25x + x2 = 0 Move the constant term to the right: Add '-33.5' to each side of the equation. 33.5 + -12.25x + -33.5 + x2 = 0 + -33.5 Reorder the terms: 33.5 + -33.5 + -12.25x + x2 = 0 + -33.5 Combine like terms: 33.5 + -33.5 = 0.0 0.0 + -12.25x + x2 = 0 + -33.5 -12.25x + x2 = 0 + -33.5 Combine like terms: 0 + -33.5 = -33.5 -12.25x + x2 = -33.5 The x term is -12.25x. Take half its coefficient (-6.125). Square it (37.515625) and add it to both sides. Add '37.515625' to each side of the equation. -12.25x + 37.515625 + x2 = -33.5 + 37.515625 Reorder the terms: 37.515625 + -12.25x + x2 = -33.5 + 37.515625 Combine like terms: -33.5 + 37.515625 = 4.015625 37.515625 + -12.25x + x2 = 4.015625 Factor a perfect square on the left side: (x + -6.125)(x + -6.125) = 4.015625 Calculate the square root of the right side: 2.003902443 Break this problem into two subproblems by setting (x + -6.125) equal to 2.003902443 and -2.003902443.Subproblem 1
x + -6.125 = 2.003902443 Simplifying x + -6.125 = 2.003902443 Reorder the terms: -6.125 + x = 2.003902443 Solving -6.125 + x = 2.003902443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = 2.003902443 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = 2.003902443 + 6.125 x = 2.003902443 + 6.125 Combine like terms: 2.003902443 + 6.125 = 8.128902443 x = 8.128902443 Simplifying x = 8.128902443Subproblem 2
x + -6.125 = -2.003902443 Simplifying x + -6.125 = -2.003902443 Reorder the terms: -6.125 + x = -2.003902443 Solving -6.125 + x = -2.003902443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = -2.003902443 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = -2.003902443 + 6.125 x = -2.003902443 + 6.125 Combine like terms: -2.003902443 + 6.125 = 4.121097557 x = 4.121097557 Simplifying x = 4.121097557Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.128902443, 4.121097557}
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