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Simplifying 7x2 + -32x + -21 = 0 Reorder the terms: -21 + -32x + 7x2 = 0 Solving -21 + -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'. -3 + -4.571428571x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -4.571428571x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -4.571428571x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4.571428571x + x2 = 0 + 3 -4.571428571x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4.571428571x + x2 = 3 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 = 3 + 5.224489797 Reorder the terms: 5.224489797 + -4.571428571x + x2 = 3 + 5.224489797 Combine like terms: 3 + 5.224489797 = 8.224489797 5.224489797 + -4.571428571x + x2 = 8.224489797 Factor a perfect square on the left side: (x + -2.285714286)(x + -2.285714286) = 8.224489797 Calculate the square root of the right side: 2.867837129 Break this problem into two subproblems by setting (x + -2.285714286) equal to 2.867837129 and -2.867837129.Subproblem 1
x + -2.285714286 = 2.867837129 Simplifying x + -2.285714286 = 2.867837129 Reorder the terms: -2.285714286 + x = 2.867837129 Solving -2.285714286 + x = 2.867837129 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 = 2.867837129 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + x = 2.867837129 + 2.285714286 x = 2.867837129 + 2.285714286 Combine like terms: 2.867837129 + 2.285714286 = 5.153551415 x = 5.153551415 Simplifying x = 5.153551415Subproblem 2
x + -2.285714286 = -2.867837129 Simplifying x + -2.285714286 = -2.867837129 Reorder the terms: -2.285714286 + x = -2.867837129 Solving -2.285714286 + x = -2.867837129 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 = -2.867837129 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + x = -2.867837129 + 2.285714286 x = -2.867837129 + 2.285714286 Combine like terms: -2.867837129 + 2.285714286 = -0.582122843 x = -0.582122843 Simplifying x = -0.582122843Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.153551415, -0.582122843}
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