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Simplifying 16x2 + 32x + 9 = 0 Reorder the terms: 9 + 32x + 16x2 = 0 Solving 9 + 32x + 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 + 2x + x2 = 0 Move the constant term to the right: Add '-0.5625' to each side of the equation. 0.5625 + 2x + -0.5625 + x2 = 0 + -0.5625 Reorder the terms: 0.5625 + -0.5625 + 2x + x2 = 0 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + 2x + x2 = 0 + -0.5625 2x + x2 = 0 + -0.5625 Combine like terms: 0 + -0.5625 = -0.5625 2x + x2 = -0.5625 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.5625 + 1 Reorder the terms: 1 + 2x + x2 = -0.5625 + 1 Combine like terms: -0.5625 + 1 = 0.4375 1 + 2x + x2 = 0.4375 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.4375 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (x + 1) equal to 0.661437828 and -0.661437828.Subproblem 1
x + 1 = 0.661437828 Simplifying x + 1 = 0.661437828 Reorder the terms: 1 + x = 0.661437828 Solving 1 + x = 0.661437828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.661437828 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.661437828 + -1 x = 0.661437828 + -1 Combine like terms: 0.661437828 + -1 = -0.338562172 x = -0.338562172 Simplifying x = -0.338562172Subproblem 2
x + 1 = -0.661437828 Simplifying x + 1 = -0.661437828 Reorder the terms: 1 + x = -0.661437828 Solving 1 + x = -0.661437828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.661437828 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.661437828 + -1 x = -0.661437828 + -1 Combine like terms: -0.661437828 + -1 = -1.661437828 x = -1.661437828 Simplifying x = -1.661437828Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.338562172, -1.661437828}
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