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Simplifying 4x2 + -49x + 65 = 0 Reorder the terms: 65 + -49x + 4x2 = 0 Solving 65 + -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'. 16.25 + -12.25x + x2 = 0 Move the constant term to the right: Add '-16.25' to each side of the equation. 16.25 + -12.25x + -16.25 + x2 = 0 + -16.25 Reorder the terms: 16.25 + -16.25 + -12.25x + x2 = 0 + -16.25 Combine like terms: 16.25 + -16.25 = 0.00 0.00 + -12.25x + x2 = 0 + -16.25 -12.25x + x2 = 0 + -16.25 Combine like terms: 0 + -16.25 = -16.25 -12.25x + x2 = -16.25 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 = -16.25 + 37.515625 Reorder the terms: 37.515625 + -12.25x + x2 = -16.25 + 37.515625 Combine like terms: -16.25 + 37.515625 = 21.265625 37.515625 + -12.25x + x2 = 21.265625 Factor a perfect square on the left side: (x + -6.125)(x + -6.125) = 21.265625 Calculate the square root of the right side: 4.611466686 Break this problem into two subproblems by setting (x + -6.125) equal to 4.611466686 and -4.611466686.Subproblem 1
x + -6.125 = 4.611466686 Simplifying x + -6.125 = 4.611466686 Reorder the terms: -6.125 + x = 4.611466686 Solving -6.125 + x = 4.611466686 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 = 4.611466686 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = 4.611466686 + 6.125 x = 4.611466686 + 6.125 Combine like terms: 4.611466686 + 6.125 = 10.736466686 x = 10.736466686 Simplifying x = 10.736466686Subproblem 2
x + -6.125 = -4.611466686 Simplifying x + -6.125 = -4.611466686 Reorder the terms: -6.125 + x = -4.611466686 Solving -6.125 + x = -4.611466686 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 = -4.611466686 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = -4.611466686 + 6.125 x = -4.611466686 + 6.125 Combine like terms: -4.611466686 + 6.125 = 1.513533314 x = 1.513533314 Simplifying x = 1.513533314Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.736466686, 1.513533314}
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