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Simplifying 20 = 16x2 + 29x + 3.8 Reorder the terms: 20 = 3.8 + 29x + 16x2 Solving 20 = 3.8 + 29x + 16x2 Solving for variable 'x'. Combine like terms: 20 + -3.8 = 16.2 16.2 + -29x + -16x2 = 3.8 + 29x + 16x2 + -3.8 + -29x + -16x2 Reorder the terms: 16.2 + -29x + -16x2 = 3.8 + -3.8 + 29x + -29x + 16x2 + -16x2 Combine like terms: 3.8 + -3.8 = 0.0 16.2 + -29x + -16x2 = 0.0 + 29x + -29x + 16x2 + -16x2 16.2 + -29x + -16x2 = 29x + -29x + 16x2 + -16x2 Combine like terms: 29x + -29x = 0 16.2 + -29x + -16x2 = 0 + 16x2 + -16x2 16.2 + -29x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 16.2 + -29x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -1.0125 + 1.8125x + x2 = 0 Move the constant term to the right: Add '1.0125' to each side of the equation. -1.0125 + 1.8125x + 1.0125 + x2 = 0 + 1.0125 Reorder the terms: -1.0125 + 1.0125 + 1.8125x + x2 = 0 + 1.0125 Combine like terms: -1.0125 + 1.0125 = 0.0000 0.0000 + 1.8125x + x2 = 0 + 1.0125 1.8125x + x2 = 0 + 1.0125 Combine like terms: 0 + 1.0125 = 1.0125 1.8125x + x2 = 1.0125 The x term is 1.8125x. Take half its coefficient (0.90625). Square it (0.8212890625) and add it to both sides. Add '0.8212890625' to each side of the equation. 1.8125x + 0.8212890625 + x2 = 1.0125 + 0.8212890625 Reorder the terms: 0.8212890625 + 1.8125x + x2 = 1.0125 + 0.8212890625 Combine like terms: 1.0125 + 0.8212890625 = 1.8337890625 0.8212890625 + 1.8125x + x2 = 1.8337890625 Factor a perfect square on the left side: (x + 0.90625)(x + 0.90625) = 1.8337890625 Calculate the square root of the right side: 1.354174679 Break this problem into two subproblems by setting (x + 0.90625) equal to 1.354174679 and -1.354174679.Subproblem 1
x + 0.90625 = 1.354174679 Simplifying x + 0.90625 = 1.354174679 Reorder the terms: 0.90625 + x = 1.354174679 Solving 0.90625 + x = 1.354174679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.90625' to each side of the equation. 0.90625 + -0.90625 + x = 1.354174679 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + x = 1.354174679 + -0.90625 x = 1.354174679 + -0.90625 Combine like terms: 1.354174679 + -0.90625 = 0.447924679 x = 0.447924679 Simplifying x = 0.447924679Subproblem 2
x + 0.90625 = -1.354174679 Simplifying x + 0.90625 = -1.354174679 Reorder the terms: 0.90625 + x = -1.354174679 Solving 0.90625 + x = -1.354174679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.90625' to each side of the equation. 0.90625 + -0.90625 + x = -1.354174679 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + x = -1.354174679 + -0.90625 x = -1.354174679 + -0.90625 Combine like terms: -1.354174679 + -0.90625 = -2.260424679 x = -2.260424679 Simplifying x = -2.260424679Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.447924679, -2.260424679}
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