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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 = 0.582122843 x = 0.582122843 Simplifying x = 0.582122843Subproblem 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 = -5.153551415 x = -5.153551415 Simplifying x = -5.153551415Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.582122843, -5.153551415}
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