Solve the following quadratic equation by completing the square method;(a)x square plus 8x-7=0 (b) 5xsquare plus 5x=2
gee - real math is a lot easier to read
x^2+8x-7 = 0
x^2+8x+16 = 7+16
(x+4)^2 = 23
x+4 = ±√23
x = -4±√23
Now you try the 2nd one...
No solve the first one to give you -8.80
5 x^2 + 5 x = 2 ? no, the answer is not 0
x^2 + x = 2/5
x^2 + x + 1/4 = 2/5 + 1/4 = (8 + 5)/20 =13/20
(x+1/2)^2 = 13/20
x + 1/2 = sqrt (13/20)
x = sqrt (13/20) - 1/2
or
x = - sqrt(13/20 - 1/2
Anonymous the final answer is suppose to be 8.80
Anyone
Hi guys
To solve a quadratic equation using the completing the square method, follow these steps:
(a) x² + 8x - 7 = 0:
Step 1: Move the constant term to the other side of the equation.
x² + 8x = 7.
Step 2: Divide the coefficient of x² by 2 and square the result.
Coefficient of x² = 1/1 = 1.
(1/2)^2 = 1/4.
Step 3: Add the value obtained in step 2 to both sides of the equation.
x² + 8x + 1/4 = 7 + 1/4.
x² + 8x + 1/4 = 29/4.
Step 4: Convert the left side of the equation into a perfect square.
(x + 1/2)² = 29/4.
Step 5: Take the square root of both sides.
x + 1/2 = ±√(29/4).
Step 6: Solve for x.
x = -1/2 ± √(29/4).
(b) 5x² + 5x = 2:
Step 1: Move the constant term to the other side of the equation.
5x² + 5x - 2 = 0.
Step 2: Divide the coefficient of x² by 2 and square the result.
Coefficient of x² = 5.
(5/2)^2 = 25/4.
Step 3: Add the value obtained in step 2 to both sides of the equation.
5x² + 5x + 25/4 = 2 + 25/4.
5x² + 5x + 25/4 = 33/4.
Step 4: Convert the left side of the equation into a perfect square.
(√5x + √(25/4))^2 = 33/4.
Step 5: Take the square root of both sides.
√5x + √(25/4) = ±√(33/4).
Step 6: Solve for x.
√5x = -√(25/4) ±√(33/4).
x = (-√(25/4) ±√(33/4)) / √5.
Therefore, the solution to the quadratic equations are:
(a) x = -1/2 ± √(29/4).
(b) x = (-√(25/4) ±√(33/4)) / √5.