Use square method to solve this quadratic equation X^2+8X-7=0
Just a variation of your last post, when you were Dan
x^2 + 8x = 7
x^2 + 8x + 16 = 7 + 16
continue....
Please help to finish it
x^2 + 8x + 16 = 7 + 16
(x+4)^2 = 23 , now take the square root of both sides
x + 4 = ±√23
x = -4 ± √23
Is that all
To solve the quadratic equation X^2 + 8X - 7 = 0 using the square method, we need to follow these steps:
Step 1: Identify the coefficients of the quadratic equation.
In this equation, the coefficient of X^2 is 1, the coefficient of X is 8, and the constant term is -7.
Step 2: Rewrite the equation in the standard form.
Rearrange the equation so that the X^2 term comes first, then the X term, and lastly the constant term. The standard form of a quadratic equation is ax^2 + bx + c = 0.
So, the equation X^2 + 8X - 7 = 0 is already in standard form.
Step 3: Complete the square.
To complete the square, we need to add a constant term to both sides of the equation. The constant term is the square of half the coefficient of the X term. In this case, the coefficient of X is 8, so half of it is 4, and its square is 16.
Adding 16 to both sides of the equation, we get:
X^2 + 8X - 7 + 16 = 0 + 16
Simplifying, we have:
X^2 + 8X + 9 = 16
Step 4: Factor and simplify.
Next, we can factor the left side of the equation, which will allow us to rewrite it as a perfect square:
(X + 3)(X + 3) = 16
Simplifying further, we have:
(X + 3)^2 = 16
Step 5: Solve for X.
Now, we can take the square root of both sides to solve for X:
√((X + 3)^2) = √(16)
Taking the square root gives us two possible solutions:
X + 3 = 4 or X + 3 = -4
Solving for X in each case:
X = 4 - 3 or X = -4 - 3
Simplifying further, we find the final solutions:
X = 1 or X = -7
Therefore, the solutions to the quadratic equation X^2 + 8X - 7 = 0 using the square method are X = 1 and X = -7.