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Simplifying 7x2 + -45x + -343 = 0 Reorder the terms: -343 + -45x + 7x2 = 0 Solving -343 + -45x + 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'. -49 + -6.428571429x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + -6.428571429x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -6.428571429x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -6.428571429x + x2 = 0 + 49 -6.428571429x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -6.428571429x + x2 = 49 The x term is -6.428571429x. Take half its coefficient (-3.214285715). Square it (10.33163266) and add it to both sides. Add '10.33163266' to each side of the equation. -6.428571429x + 10.33163266 + x2 = 49 + 10.33163266 Reorder the terms: 10.33163266 + -6.428571429x + x2 = 49 + 10.33163266 Combine like terms: 49 + 10.33163266 = 59.33163266 10.33163266 + -6.428571429x + x2 = 59.33163266 Factor a perfect square on the left side: (x + -3.214285715)(x + -3.214285715) = 59.33163266 Calculate the square root of the right side: 7.702702945 Break this problem into two subproblems by setting (x + -3.214285715) equal to 7.702702945 and -7.702702945.Subproblem 1
x + -3.214285715 = 7.702702945 Simplifying x + -3.214285715 = 7.702702945 Reorder the terms: -3.214285715 + x = 7.702702945 Solving -3.214285715 + x = 7.702702945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.214285715' to each side of the equation. -3.214285715 + 3.214285715 + x = 7.702702945 + 3.214285715 Combine like terms: -3.214285715 + 3.214285715 = 0.000000000 0.000000000 + x = 7.702702945 + 3.214285715 x = 7.702702945 + 3.214285715 Combine like terms: 7.702702945 + 3.214285715 = 10.91698866 x = 10.91698866 Simplifying x = 10.91698866Subproblem 2
x + -3.214285715 = -7.702702945 Simplifying x + -3.214285715 = -7.702702945 Reorder the terms: -3.214285715 + x = -7.702702945 Solving -3.214285715 + x = -7.702702945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.214285715' to each side of the equation. -3.214285715 + 3.214285715 + x = -7.702702945 + 3.214285715 Combine like terms: -3.214285715 + 3.214285715 = 0.000000000 0.000000000 + x = -7.702702945 + 3.214285715 x = -7.702702945 + 3.214285715 Combine like terms: -7.702702945 + 3.214285715 = -4.48841723 x = -4.48841723 Simplifying x = -4.48841723Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.91698866, -4.48841723}
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