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Simplifying 7x2 + -141x + -30 = 0 Reorder the terms: -30 + -141x + 7x2 = 0 Solving -30 + -141x + 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'. -4.285714286 + -20.14285714x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + -20.14285714x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + -20.14285714x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + -20.14285714x + x2 = 0 + 4.285714286 -20.14285714x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 -20.14285714x + x2 = 4.285714286 The x term is -20.14285714x. Take half its coefficient (-10.07142857). Square it (101.4336734) and add it to both sides. Add '101.4336734' to each side of the equation. -20.14285714x + 101.4336734 + x2 = 4.285714286 + 101.4336734 Reorder the terms: 101.4336734 + -20.14285714x + x2 = 4.285714286 + 101.4336734 Combine like terms: 4.285714286 + 101.4336734 = 105.719387686 101.4336734 + -20.14285714x + x2 = 105.719387686 Factor a perfect square on the left side: (x + -10.07142857)(x + -10.07142857) = 105.719387686 Calculate the square root of the right side: 10.281993371 Break this problem into two subproblems by setting (x + -10.07142857) equal to 10.281993371 and -10.281993371.Subproblem 1
x + -10.07142857 = 10.281993371 Simplifying x + -10.07142857 = 10.281993371 Reorder the terms: -10.07142857 + x = 10.281993371 Solving -10.07142857 + x = 10.281993371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.07142857' to each side of the equation. -10.07142857 + 10.07142857 + x = 10.281993371 + 10.07142857 Combine like terms: -10.07142857 + 10.07142857 = 0.00000000 0.00000000 + x = 10.281993371 + 10.07142857 x = 10.281993371 + 10.07142857 Combine like terms: 10.281993371 + 10.07142857 = 20.353421941 x = 20.353421941 Simplifying x = 20.353421941Subproblem 2
x + -10.07142857 = -10.281993371 Simplifying x + -10.07142857 = -10.281993371 Reorder the terms: -10.07142857 + x = -10.281993371 Solving -10.07142857 + x = -10.281993371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.07142857' to each side of the equation. -10.07142857 + 10.07142857 + x = -10.281993371 + 10.07142857 Combine like terms: -10.07142857 + 10.07142857 = 0.00000000 0.00000000 + x = -10.281993371 + 10.07142857 x = -10.281993371 + 10.07142857 Combine like terms: -10.281993371 + 10.07142857 = -0.210564801 x = -0.210564801 Simplifying x = -0.210564801Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.353421941, -0.210564801}
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