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Simplifying 3x2 + -5x + 4 = 50 Reorder the terms: 4 + -5x + 3x2 = 50 Solving 4 + -5x + 3x2 = 50 Solving for variable 'x'. Reorder the terms: 4 + -50 + -5x + 3x2 = 50 + -50 Combine like terms: 4 + -50 = -46 -46 + -5x + 3x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -46 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -15.33333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '15.33333333' to each side of the equation. -15.33333333 + -1.666666667x + 15.33333333 + x2 = 0 + 15.33333333 Reorder the terms: -15.33333333 + 15.33333333 + -1.666666667x + x2 = 0 + 15.33333333 Combine like terms: -15.33333333 + 15.33333333 = 0.00000000 0.00000000 + -1.666666667x + x2 = 0 + 15.33333333 -1.666666667x + x2 = 0 + 15.33333333 Combine like terms: 0 + 15.33333333 = 15.33333333 -1.666666667x + x2 = 15.33333333 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 15.33333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 15.33333333 + 0.6944444447 Combine like terms: 15.33333333 + 0.6944444447 = 16.0277777747 0.6944444447 + -1.666666667x + x2 = 16.0277777747 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 16.0277777747 Calculate the square root of the right side: 4.003470716 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 4.003470716 and -4.003470716.Subproblem 1
x + -0.8333333335 = 4.003470716 Simplifying x + -0.8333333335 = 4.003470716 Reorder the terms: -0.8333333335 + x = 4.003470716 Solving -0.8333333335 + x = 4.003470716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 4.003470716 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 4.003470716 + 0.8333333335 x = 4.003470716 + 0.8333333335 Combine like terms: 4.003470716 + 0.8333333335 = 4.8368040495 x = 4.8368040495 Simplifying x = 4.8368040495Subproblem 2
x + -0.8333333335 = -4.003470716 Simplifying x + -0.8333333335 = -4.003470716 Reorder the terms: -0.8333333335 + x = -4.003470716 Solving -0.8333333335 + x = -4.003470716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -4.003470716 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -4.003470716 + 0.8333333335 x = -4.003470716 + 0.8333333335 Combine like terms: -4.003470716 + 0.8333333335 = -3.1701373825 x = -3.1701373825 Simplifying x = -3.1701373825Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.8368040495, -3.1701373825}
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