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Simplifying 4x2 + -44x + 119 = 0 Reorder the terms: 119 + -44x + 4x2 = 0 Solving 119 + -44x + 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'. 29.75 + -11x + x2 = 0 Move the constant term to the right: Add '-29.75' to each side of the equation. 29.75 + -11x + -29.75 + x2 = 0 + -29.75 Reorder the terms: 29.75 + -29.75 + -11x + x2 = 0 + -29.75 Combine like terms: 29.75 + -29.75 = 0.00 0.00 + -11x + x2 = 0 + -29.75 -11x + x2 = 0 + -29.75 Combine like terms: 0 + -29.75 = -29.75 -11x + x2 = -29.75 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -29.75 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -29.75 + 30.25 Combine like terms: -29.75 + 30.25 = 0.5 30.25 + -11x + x2 = 0.5 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + -5.5) equal to 0.707106781 and -0.707106781.Subproblem 1
x + -5.5 = 0.707106781 Simplifying x + -5.5 = 0.707106781 Reorder the terms: -5.5 + x = 0.707106781 Solving -5.5 + x = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 0.707106781 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 0.707106781 + 5.5 x = 0.707106781 + 5.5 Combine like terms: 0.707106781 + 5.5 = 6.207106781 x = 6.207106781 Simplifying x = 6.207106781Subproblem 2
x + -5.5 = -0.707106781 Simplifying x + -5.5 = -0.707106781 Reorder the terms: -5.5 + x = -0.707106781 Solving -5.5 + x = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -0.707106781 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -0.707106781 + 5.5 x = -0.707106781 + 5.5 Combine like terms: -0.707106781 + 5.5 = 4.792893219 x = 4.792893219 Simplifying x = 4.792893219Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.207106781, 4.792893219}
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