solve the following equation by completing square
x(square) + 5x - 84
Pls show steps
x= or x=
x^2 + 5x - 84 = 0
x^2 + 5x + (5/2)^2 - 84 - (5/2)^2 = 0
(x + 5/2)^2 = 361/4
x + 5/2 = ±19/2
x = -5/2 ± 19/2
x = -12, 7
To solve the quadratic equation by completing the square, follow these steps:
1. Start with the equation: x^2 + 5x - 84 = 0.
2. Move the constant term to the other side of the equation: x^2 + 5x = 84.
3. Take half of the coefficient of the x-term (5/2) and square it to get (5/2)^2 = 25/4.
4. Add the result from step 3 to both sides of the equation: x^2 + 5x + 25/4 = 84 + 25/4.
5. Simplify the right side of the equation: x^2 + 5x + 25/4 = 336/4 + 25/4.
This becomes: x^2 + 5x + 25/4 = 361/4.
6. Rewrite the left side of the equation as a perfect square trinomial: (x + 5/2)^2 = 361/4.
7. Take the square root of both sides of the equation: √((x + 5/2)^2) = ±√(361/4).
This simplifies to: x + 5/2 = ±19/2.
8. Solve for x by isolating it on one side of the equation: x = -5/2 ± 19/2.
9. Simplify the expression for x: x = (-5 ± 19)/2.
This gives two possible solutions: x = (-5 + 19)/2 and x = (-5 - 19)/2.
10. Simplify each solution: x = 14/2 and x = -24/2.
Therefore, the solutions to the equation x^2 + 5x - 84 = 0 are x = 7 and x = -12.
So, x = 7 or x = -12.