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Simplifying 28x2 + 17x + -3 = 6 Reorder the terms: -3 + 17x + 28x2 = 6 Solving -3 + 17x + 28x2 = 6 Solving for variable 'x'. Reorder the terms: -3 + -6 + 17x + 28x2 = 6 + -6 Combine like terms: -3 + -6 = -9 -9 + 17x + 28x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -9 + 17x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.3214285714 + 0.6071428571x + x2 = 0 Move the constant term to the right: Add '0.3214285714' to each side of the equation. -0.3214285714 + 0.6071428571x + 0.3214285714 + x2 = 0 + 0.3214285714 Reorder the terms: -0.3214285714 + 0.3214285714 + 0.6071428571x + x2 = 0 + 0.3214285714 Combine like terms: -0.3214285714 + 0.3214285714 = 0.0000000000 0.0000000000 + 0.6071428571x + x2 = 0 + 0.3214285714 0.6071428571x + x2 = 0 + 0.3214285714 Combine like terms: 0 + 0.3214285714 = 0.3214285714 0.6071428571x + x2 = 0.3214285714 The x term is 0.6071428571x. Take half its coefficient (0.3035714286). Square it (0.09215561226) and add it to both sides. Add '0.09215561226' to each side of the equation. 0.6071428571x + 0.09215561226 + x2 = 0.3214285714 + 0.09215561226 Reorder the terms: 0.09215561226 + 0.6071428571x + x2 = 0.3214285714 + 0.09215561226 Combine like terms: 0.3214285714 + 0.09215561226 = 0.41358418366 0.09215561226 + 0.6071428571x + x2 = 0.41358418366 Factor a perfect square on the left side: (x + 0.3035714286)(x + 0.3035714286) = 0.41358418366 Calculate the square root of the right side: 0.643105111 Break this problem into two subproblems by setting (x + 0.3035714286) equal to 0.643105111 and -0.643105111.Subproblem 1
x + 0.3035714286 = 0.643105111 Simplifying x + 0.3035714286 = 0.643105111 Reorder the terms: 0.3035714286 + x = 0.643105111 Solving 0.3035714286 + x = 0.643105111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3035714286' to each side of the equation. 0.3035714286 + -0.3035714286 + x = 0.643105111 + -0.3035714286 Combine like terms: 0.3035714286 + -0.3035714286 = 0.0000000000 0.0000000000 + x = 0.643105111 + -0.3035714286 x = 0.643105111 + -0.3035714286 Combine like terms: 0.643105111 + -0.3035714286 = 0.3395336824 x = 0.3395336824 Simplifying x = 0.3395336824Subproblem 2
x + 0.3035714286 = -0.643105111 Simplifying x + 0.3035714286 = -0.643105111 Reorder the terms: 0.3035714286 + x = -0.643105111 Solving 0.3035714286 + x = -0.643105111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3035714286' to each side of the equation. 0.3035714286 + -0.3035714286 + x = -0.643105111 + -0.3035714286 Combine like terms: 0.3035714286 + -0.3035714286 = 0.0000000000 0.0000000000 + x = -0.643105111 + -0.3035714286 x = -0.643105111 + -0.3035714286 Combine like terms: -0.643105111 + -0.3035714286 = -0.9466765396 x = -0.9466765396 Simplifying x = -0.9466765396Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3395336824, -0.9466765396}
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