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Simplifying 16x2 + 28x + 9 = 0 Reorder the terms: 9 + 28x + 16x2 = 0 Solving 9 + 28x + 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 + 1.75x + x2 = 0 Move the constant term to the right: Add '-0.5625' to each side of the equation. 0.5625 + 1.75x + -0.5625 + x2 = 0 + -0.5625 Reorder the terms: 0.5625 + -0.5625 + 1.75x + x2 = 0 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + 1.75x + x2 = 0 + -0.5625 1.75x + x2 = 0 + -0.5625 Combine like terms: 0 + -0.5625 = -0.5625 1.75x + x2 = -0.5625 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = -0.5625 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = -0.5625 + 0.765625 Combine like terms: -0.5625 + 0.765625 = 0.203125 0.765625 + 1.75x + x2 = 0.203125 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 0.203125 Calculate the square root of the right side: 0.450693909 Break this problem into two subproblems by setting (x + 0.875) equal to 0.450693909 and -0.450693909.Subproblem 1
x + 0.875 = 0.450693909 Simplifying x + 0.875 = 0.450693909 Reorder the terms: 0.875 + x = 0.450693909 Solving 0.875 + x = 0.450693909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 0.450693909 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 0.450693909 + -0.875 x = 0.450693909 + -0.875 Combine like terms: 0.450693909 + -0.875 = -0.424306091 x = -0.424306091 Simplifying x = -0.424306091Subproblem 2
x + 0.875 = -0.450693909 Simplifying x + 0.875 = -0.450693909 Reorder the terms: 0.875 + x = -0.450693909 Solving 0.875 + x = -0.450693909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -0.450693909 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -0.450693909 + -0.875 x = -0.450693909 + -0.875 Combine like terms: -0.450693909 + -0.875 = -1.325693909 x = -1.325693909 Simplifying x = -1.325693909Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.424306091, -1.325693909}
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