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Simplifying 7x2 + 61x + -73 = 0 Reorder the terms: -73 + 61x + 7x2 = 0 Solving -73 + 61x + 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'. -10.42857143 + 8.714285714x + x2 = 0 Move the constant term to the right: Add '10.42857143' to each side of the equation. -10.42857143 + 8.714285714x + 10.42857143 + x2 = 0 + 10.42857143 Reorder the terms: -10.42857143 + 10.42857143 + 8.714285714x + x2 = 0 + 10.42857143 Combine like terms: -10.42857143 + 10.42857143 = 0.00000000 0.00000000 + 8.714285714x + x2 = 0 + 10.42857143 8.714285714x + x2 = 0 + 10.42857143 Combine like terms: 0 + 10.42857143 = 10.42857143 8.714285714x + x2 = 10.42857143 The x term is 8.714285714x. Take half its coefficient (4.357142857). Square it (18.98469388) and add it to both sides. Add '18.98469388' to each side of the equation. 8.714285714x + 18.98469388 + x2 = 10.42857143 + 18.98469388 Reorder the terms: 18.98469388 + 8.714285714x + x2 = 10.42857143 + 18.98469388 Combine like terms: 10.42857143 + 18.98469388 = 29.41326531 18.98469388 + 8.714285714x + x2 = 29.41326531 Factor a perfect square on the left side: (x + 4.357142857)(x + 4.357142857) = 29.41326531 Calculate the square root of the right side: 5.423399793 Break this problem into two subproblems by setting (x + 4.357142857) equal to 5.423399793 and -5.423399793.Subproblem 1
x + 4.357142857 = 5.423399793 Simplifying x + 4.357142857 = 5.423399793 Reorder the terms: 4.357142857 + x = 5.423399793 Solving 4.357142857 + x = 5.423399793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.357142857' to each side of the equation. 4.357142857 + -4.357142857 + x = 5.423399793 + -4.357142857 Combine like terms: 4.357142857 + -4.357142857 = 0.000000000 0.000000000 + x = 5.423399793 + -4.357142857 x = 5.423399793 + -4.357142857 Combine like terms: 5.423399793 + -4.357142857 = 1.066256936 x = 1.066256936 Simplifying x = 1.066256936Subproblem 2
x + 4.357142857 = -5.423399793 Simplifying x + 4.357142857 = -5.423399793 Reorder the terms: 4.357142857 + x = -5.423399793 Solving 4.357142857 + x = -5.423399793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.357142857' to each side of the equation. 4.357142857 + -4.357142857 + x = -5.423399793 + -4.357142857 Combine like terms: 4.357142857 + -4.357142857 = 0.000000000 0.000000000 + x = -5.423399793 + -4.357142857 x = -5.423399793 + -4.357142857 Combine like terms: -5.423399793 + -4.357142857 = -9.78054265 x = -9.78054265 Simplifying x = -9.78054265Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.066256936, -9.78054265}
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