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Simplifying 7x2 + -47x + -9 = 0 Reorder the terms: -9 + -47x + 7x2 = 0 Solving -9 + -47x + 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'. -1.285714286 + -6.714285714x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -6.714285714x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -6.714285714x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -6.714285714x + x2 = 0 + 1.285714286 -6.714285714x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -6.714285714x + x2 = 1.285714286 The x term is -6.714285714x. Take half its coefficient (-3.357142857). Square it (11.27040816) and add it to both sides. Add '11.27040816' to each side of the equation. -6.714285714x + 11.27040816 + x2 = 1.285714286 + 11.27040816 Reorder the terms: 11.27040816 + -6.714285714x + x2 = 1.285714286 + 11.27040816 Combine like terms: 1.285714286 + 11.27040816 = 12.556122446 11.27040816 + -6.714285714x + x2 = 12.556122446 Factor a perfect square on the left side: (x + -3.357142857)(x + -3.357142857) = 12.556122446 Calculate the square root of the right side: 3.54346193 Break this problem into two subproblems by setting (x + -3.357142857) equal to 3.54346193 and -3.54346193.Subproblem 1
x + -3.357142857 = 3.54346193 Simplifying x + -3.357142857 = 3.54346193 Reorder the terms: -3.357142857 + x = 3.54346193 Solving -3.357142857 + x = 3.54346193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.357142857' to each side of the equation. -3.357142857 + 3.357142857 + x = 3.54346193 + 3.357142857 Combine like terms: -3.357142857 + 3.357142857 = 0.000000000 0.000000000 + x = 3.54346193 + 3.357142857 x = 3.54346193 + 3.357142857 Combine like terms: 3.54346193 + 3.357142857 = 6.900604787 x = 6.900604787 Simplifying x = 6.900604787Subproblem 2
x + -3.357142857 = -3.54346193 Simplifying x + -3.357142857 = -3.54346193 Reorder the terms: -3.357142857 + x = -3.54346193 Solving -3.357142857 + x = -3.54346193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.357142857' to each side of the equation. -3.357142857 + 3.357142857 + x = -3.54346193 + 3.357142857 Combine like terms: -3.357142857 + 3.357142857 = 0.000000000 0.000000000 + x = -3.54346193 + 3.357142857 x = -3.54346193 + 3.357142857 Combine like terms: -3.54346193 + 3.357142857 = -0.186319073 x = -0.186319073 Simplifying x = -0.186319073Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.900604787, -0.186319073}
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