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Simplifying 16x2 + -29x + 9 = 0 Reorder the terms: 9 + -29x + 16x2 = 0 Solving 9 + -29x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.5625 + -1.8125x + x2 = 0 Move the constant term to the right: Add '-0.5625' to each side of the equation. 0.5625 + -1.8125x + -0.5625 + x2 = 0 + -0.5625 Reorder the terms: 0.5625 + -0.5625 + -1.8125x + x2 = 0 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + -1.8125x + x2 = 0 + -0.5625 -1.8125x + x2 = 0 + -0.5625 Combine like terms: 0 + -0.5625 = -0.5625 -1.8125x + x2 = -0.5625 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 = -0.5625 + 0.8212890625 Reorder the terms: 0.8212890625 + -1.8125x + x2 = -0.5625 + 0.8212890625 Combine like terms: -0.5625 + 0.8212890625 = 0.2587890625 0.8212890625 + -1.8125x + x2 = 0.2587890625 Factor a perfect square on the left side: (x + -0.90625)(x + -0.90625) = 0.2587890625 Calculate the square root of the right side: 0.508713144 Break this problem into two subproblems by setting (x + -0.90625) equal to 0.508713144 and -0.508713144.Subproblem 1
x + -0.90625 = 0.508713144 Simplifying x + -0.90625 = 0.508713144 Reorder the terms: -0.90625 + x = 0.508713144 Solving -0.90625 + x = 0.508713144 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 = 0.508713144 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = 0.508713144 + 0.90625 x = 0.508713144 + 0.90625 Combine like terms: 0.508713144 + 0.90625 = 1.414963144 x = 1.414963144 Simplifying x = 1.414963144Subproblem 2
x + -0.90625 = -0.508713144 Simplifying x + -0.90625 = -0.508713144 Reorder the terms: -0.90625 + x = -0.508713144 Solving -0.90625 + x = -0.508713144 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 = -0.508713144 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = -0.508713144 + 0.90625 x = -0.508713144 + 0.90625 Combine like terms: -0.508713144 + 0.90625 = 0.397536856 x = 0.397536856 Simplifying x = 0.397536856Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.414963144, 0.397536856}
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