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Simplifying 16x2 + 6x + -9 = 0 Reorder the terms: -9 + 6x + 16x2 = 0 Solving -9 + 6x + 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 + 0.375x + x2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + 0.375x + 0.5625 + x2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + 0.375x + x2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + 0.375x + x2 = 0 + 0.5625 0.375x + x2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 0.375x + x2 = 0.5625 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 0.5625 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 0.5625 + 0.03515625 Combine like terms: 0.5625 + 0.03515625 = 0.59765625 0.03515625 + 0.375x + x2 = 0.59765625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 0.59765625 Calculate the square root of the right side: 0.773082305 Break this problem into two subproblems by setting (x + 0.1875) equal to 0.773082305 and -0.773082305.Subproblem 1
x + 0.1875 = 0.773082305 Simplifying x + 0.1875 = 0.773082305 Reorder the terms: 0.1875 + x = 0.773082305 Solving 0.1875 + x = 0.773082305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 0.773082305 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 0.773082305 + -0.1875 x = 0.773082305 + -0.1875 Combine like terms: 0.773082305 + -0.1875 = 0.585582305 x = 0.585582305 Simplifying x = 0.585582305Subproblem 2
x + 0.1875 = -0.773082305 Simplifying x + 0.1875 = -0.773082305 Reorder the terms: 0.1875 + x = -0.773082305 Solving 0.1875 + x = -0.773082305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -0.773082305 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -0.773082305 + -0.1875 x = -0.773082305 + -0.1875 Combine like terms: -0.773082305 + -0.1875 = -0.960582305 x = -0.960582305 Simplifying x = -0.960582305Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.585582305, -0.960582305}
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