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Simplifying 4x2 + -36x + 79 = 0 Reorder the terms: 79 + -36x + 4x2 = 0 Solving 79 + -36x + 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'. 19.75 + -9x + x2 = 0 Move the constant term to the right: Add '-19.75' to each side of the equation. 19.75 + -9x + -19.75 + x2 = 0 + -19.75 Reorder the terms: 19.75 + -19.75 + -9x + x2 = 0 + -19.75 Combine like terms: 19.75 + -19.75 = 0.00 0.00 + -9x + x2 = 0 + -19.75 -9x + x2 = 0 + -19.75 Combine like terms: 0 + -19.75 = -19.75 -9x + x2 = -19.75 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -19.75 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -19.75 + 20.25 Combine like terms: -19.75 + 20.25 = 0.5 20.25 + -9x + x2 = 0.5 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + -4.5) equal to 0.707106781 and -0.707106781.Subproblem 1
x + -4.5 = 0.707106781 Simplifying x + -4.5 = 0.707106781 Reorder the terms: -4.5 + x = 0.707106781 Solving -4.5 + x = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 0.707106781 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 0.707106781 + 4.5 x = 0.707106781 + 4.5 Combine like terms: 0.707106781 + 4.5 = 5.207106781 x = 5.207106781 Simplifying x = 5.207106781Subproblem 2
x + -4.5 = -0.707106781 Simplifying x + -4.5 = -0.707106781 Reorder the terms: -4.5 + x = -0.707106781 Solving -4.5 + x = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -0.707106781 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -0.707106781 + 4.5 x = -0.707106781 + 4.5 Combine like terms: -0.707106781 + 4.5 = 3.792893219 x = 3.792893219 Simplifying x = 3.792893219Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.207106781, 3.792893219}
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