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Simplifying 6x * 6x + -17x + -14 = 0 Reorder the terms for easier multiplication: 6 * 6x * x + -17x + -14 = 0 Multiply 6 * 6 36x * x + -17x + -14 = 0 Multiply x * x 36x2 + -17x + -14 = 0 Reorder the terms: -14 + -17x + 36x2 = 0 Solving -14 + -17x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.3888888889 + -0.4722222222x + x2 = 0 Move the constant term to the right: Add '0.3888888889' to each side of the equation. -0.3888888889 + -0.4722222222x + 0.3888888889 + x2 = 0 + 0.3888888889 Reorder the terms: -0.3888888889 + 0.3888888889 + -0.4722222222x + x2 = 0 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + -0.4722222222x + x2 = 0 + 0.3888888889 -0.4722222222x + x2 = 0 + 0.3888888889 Combine like terms: 0 + 0.3888888889 = 0.3888888889 -0.4722222222x + x2 = 0.3888888889 The x term is -0.4722222222x. Take half its coefficient (-0.2361111111). Square it (0.05574845678) and add it to both sides. Add '0.05574845678' to each side of the equation. -0.4722222222x + 0.05574845678 + x2 = 0.3888888889 + 0.05574845678 Reorder the terms: 0.05574845678 + -0.4722222222x + x2 = 0.3888888889 + 0.05574845678 Combine like terms: 0.3888888889 + 0.05574845678 = 0.44463734568 0.05574845678 + -0.4722222222x + x2 = 0.44463734568 Factor a perfect square on the left side: (x + -0.2361111111)(x + -0.2361111111) = 0.44463734568 Calculate the square root of the right side: 0.666811327 Break this problem into two subproblems by setting (x + -0.2361111111) equal to 0.666811327 and -0.666811327.Subproblem 1
x + -0.2361111111 = 0.666811327 Simplifying x + -0.2361111111 = 0.666811327 Reorder the terms: -0.2361111111 + x = 0.666811327 Solving -0.2361111111 + x = 0.666811327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2361111111' to each side of the equation. -0.2361111111 + 0.2361111111 + x = 0.666811327 + 0.2361111111 Combine like terms: -0.2361111111 + 0.2361111111 = 0.0000000000 0.0000000000 + x = 0.666811327 + 0.2361111111 x = 0.666811327 + 0.2361111111 Combine like terms: 0.666811327 + 0.2361111111 = 0.9029224381 x = 0.9029224381 Simplifying x = 0.9029224381Subproblem 2
x + -0.2361111111 = -0.666811327 Simplifying x + -0.2361111111 = -0.666811327 Reorder the terms: -0.2361111111 + x = -0.666811327 Solving -0.2361111111 + x = -0.666811327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2361111111' to each side of the equation. -0.2361111111 + 0.2361111111 + x = -0.666811327 + 0.2361111111 Combine like terms: -0.2361111111 + 0.2361111111 = 0.0000000000 0.0000000000 + x = -0.666811327 + 0.2361111111 x = -0.666811327 + 0.2361111111 Combine like terms: -0.666811327 + 0.2361111111 = -0.4307002159 x = -0.4307002159 Simplifying x = -0.4307002159Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9029224381, -0.4307002159}
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