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Simplifying 6x * 6x + 17x + -3 = 0 Reorder the terms for easier multiplication: 6 * 6x * x + 17x + -3 = 0 Multiply 6 * 6 36x * x + 17x + -3 = 0 Multiply x * x 36x2 + 17x + -3 = 0 Reorder the terms: -3 + 17x + 36x2 = 0 Solving -3 + 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'. -0.08333333333 + 0.4722222222x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.4722222222x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.4722222222x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.4722222222x + x2 = 0 + 0.08333333333 0.4722222222x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.4722222222x + x2 = 0.08333333333 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 = 0.08333333333 + 0.05574845678 Reorder the terms: 0.05574845678 + 0.4722222222x + x2 = 0.08333333333 + 0.05574845678 Combine like terms: 0.08333333333 + 0.05574845678 = 0.13908179011 0.05574845678 + 0.4722222222x + x2 = 0.13908179011 Factor a perfect square on the left side: (x + 0.2361111111)(x + 0.2361111111) = 0.13908179011 Calculate the square root of the right side: 0.372936711 Break this problem into two subproblems by setting (x + 0.2361111111) equal to 0.372936711 and -0.372936711.Subproblem 1
x + 0.2361111111 = 0.372936711 Simplifying x + 0.2361111111 = 0.372936711 Reorder the terms: 0.2361111111 + x = 0.372936711 Solving 0.2361111111 + x = 0.372936711 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 = 0.372936711 + -0.2361111111 Combine like terms: 0.2361111111 + -0.2361111111 = 0.0000000000 0.0000000000 + x = 0.372936711 + -0.2361111111 x = 0.372936711 + -0.2361111111 Combine like terms: 0.372936711 + -0.2361111111 = 0.1368255999 x = 0.1368255999 Simplifying x = 0.1368255999Subproblem 2
x + 0.2361111111 = -0.372936711 Simplifying x + 0.2361111111 = -0.372936711 Reorder the terms: 0.2361111111 + x = -0.372936711 Solving 0.2361111111 + x = -0.372936711 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 = -0.372936711 + -0.2361111111 Combine like terms: 0.2361111111 + -0.2361111111 = 0.0000000000 0.0000000000 + x = -0.372936711 + -0.2361111111 x = -0.372936711 + -0.2361111111 Combine like terms: -0.372936711 + -0.2361111111 = -0.6090478221 x = -0.6090478221 Simplifying x = -0.6090478221Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1368255999, -0.6090478221}
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