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Simplifying 7x2 + -6x + -162 = 0 Reorder the terms: -162 + -6x + 7x2 = 0 Solving -162 + -6x + 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'. -23.14285714 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '23.14285714' to each side of the equation. -23.14285714 + -0.8571428571x + 23.14285714 + x2 = 0 + 23.14285714 Reorder the terms: -23.14285714 + 23.14285714 + -0.8571428571x + x2 = 0 + 23.14285714 Combine like terms: -23.14285714 + 23.14285714 = 0.00000000 0.00000000 + -0.8571428571x + x2 = 0 + 23.14285714 -0.8571428571x + x2 = 0 + 23.14285714 Combine like terms: 0 + 23.14285714 = 23.14285714 -0.8571428571x + x2 = 23.14285714 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = 23.14285714 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 23.14285714 + 0.1836734694 Combine like terms: 23.14285714 + 0.1836734694 = 23.3265306094 0.1836734694 + -0.8571428571x + x2 = 23.3265306094 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 23.3265306094 Calculate the square root of the right side: 4.829754715 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 4.829754715 and -4.829754715.Subproblem 1
x + -0.4285714286 = 4.829754715 Simplifying x + -0.4285714286 = 4.829754715 Reorder the terms: -0.4285714286 + x = 4.829754715 Solving -0.4285714286 + x = 4.829754715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 4.829754715 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 4.829754715 + 0.4285714286 x = 4.829754715 + 0.4285714286 Combine like terms: 4.829754715 + 0.4285714286 = 5.2583261436 x = 5.2583261436 Simplifying x = 5.2583261436Subproblem 2
x + -0.4285714286 = -4.829754715 Simplifying x + -0.4285714286 = -4.829754715 Reorder the terms: -0.4285714286 + x = -4.829754715 Solving -0.4285714286 + x = -4.829754715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -4.829754715 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -4.829754715 + 0.4285714286 x = -4.829754715 + 0.4285714286 Combine like terms: -4.829754715 + 0.4285714286 = -4.4011832864 x = -4.4011832864 Simplifying x = -4.4011832864Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.2583261436, -4.4011832864}
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