Solve by completing the square : 2x^2= 9x+5
To solve the quadratic equation 2x^2 = 9x + 5 by completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation:
2x^2 - 9x = 5
Step 2: Divide the equation by the coefficient of x^2 to make the coefficient 1:
x^2 - (9/2)x = 5/2
Step 3: Take half of the coefficient of x (which is -(9/2)) and square it: (-9/2)^2 = 81/4
Step 4: Add the result from step 3 to both sides of the equation:
x^2 - (9/2)x + 81/4 = 5/2 + 81/4
x^2 - (9/2)x + 81/4 = 41/4
Step 5: Rewrite the left side of the equation as a perfect square:
(x - (9/4))^2 = 41/4
Step 6: Take the square root of both sides of the equation and solve for x:
x - (9/4) = ±√(41/4)
x - (9/4) = ±(±√41)/2
Step 7: Solve for x by adding (9/4) to both sides of the equation:
x = (9/4) ± (±√41)/2
Therefore, the solutions to the equation 2x^2 = 9x + 5 by completing the square are:
x = (9/4) + (√41)/2 and x = (9/4) - (√41)/2
2x^2= 9x+5
2x^2 - 9x = 5
x^2 - 9/2 x = 5/2
x^2 - 9/2 x + 81/16 = 5/2 + 81/16
(x-9/4)^2 = 121/16
x-9/4 = ±11/4
x = 9/4 ± 11/4
x = -1/2 , 5
How to solve by completely the square.
X^2+18x+10=0