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Simplifying 7x2 + -32x + -12 = 0 Reorder the terms: -12 + -32x + 7x2 = 0 Solving -12 + -32x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.714285714 + -4.571428571x + x2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + -4.571428571x + 1.714285714 + x2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + -4.571428571x + x2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + -4.571428571x + x2 = 0 + 1.714285714 -4.571428571x + x2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 -4.571428571x + x2 = 1.714285714 The x term is -4.571428571x. Take half its coefficient (-2.285714286). Square it (5.224489797) and add it to both sides. Add '5.224489797' to each side of the equation. -4.571428571x + 5.224489797 + x2 = 1.714285714 + 5.224489797 Reorder the terms: 5.224489797 + -4.571428571x + x2 = 1.714285714 + 5.224489797 Combine like terms: 1.714285714 + 5.224489797 = 6.938775511 5.224489797 + -4.571428571x + x2 = 6.938775511 Factor a perfect square on the left side: (x + -2.285714286)(x + -2.285714286) = 6.938775511 Calculate the square root of the right side: 2.634155559 Break this problem into two subproblems by setting (x + -2.285714286) equal to 2.634155559 and -2.634155559.Subproblem 1
x + -2.285714286 = 2.634155559 Simplifying x + -2.285714286 = 2.634155559 Reorder the terms: -2.285714286 + x = 2.634155559 Solving -2.285714286 + x = 2.634155559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.285714286' to each side of the equation. -2.285714286 + 2.285714286 + x = 2.634155559 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + x = 2.634155559 + 2.285714286 x = 2.634155559 + 2.285714286 Combine like terms: 2.634155559 + 2.285714286 = 4.919869845 x = 4.919869845 Simplifying x = 4.919869845Subproblem 2
x + -2.285714286 = -2.634155559 Simplifying x + -2.285714286 = -2.634155559 Reorder the terms: -2.285714286 + x = -2.634155559 Solving -2.285714286 + x = -2.634155559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.285714286' to each side of the equation. -2.285714286 + 2.285714286 + x = -2.634155559 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + x = -2.634155559 + 2.285714286 x = -2.634155559 + 2.285714286 Combine like terms: -2.634155559 + 2.285714286 = -0.348441273 x = -0.348441273 Simplifying x = -0.348441273Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.919869845, -0.348441273}
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