Final answer:
To solve the quadratic equation -4x^2+5x+17=0 by completing the square, divide all terms by -4, then complete the square on the left side by adding the square of half of the x coefficient to both sides. Finally, write the left side as a perfect square and solve for x.
Step-by-step explanation:
To solve the quadratic equation -4x^2+5x+17=0 by completing the square, follow these steps:
- Move the constant term to the right side of the equation: -4x^2 + 5x = -17.
- Divide all terms by the coefficient of x^2, which is -4: x^2 - (5/4)x = 17/4.
- To complete the square, add the square of half the coefficient of x to both sides of the equation. In this case, add ((5/8)^2) to get x^2 - (5/4)x + (25/64) = 17/4 + (25/64).
- Write the left side as a perfect square: (x - (5/8))^2 = 17/4 + (25/64).
- Simplify the right side and solve for x by taking the square root of both sides, remembering to consider both the positive and negative square roots.
By completing these steps, you will find the solutions to the original equation.