Consider the following quadratic equation:
28x^2=−23x+15
Step 1 of 2 : Using the standard form ax2+bx+c=0
of the given quadratic equation, factor the left hand side of the equation into two linear factors.
To factor the left hand side of the equation 28x^2 = -23x + 15, we can first divide both sides of the equation by 28 to simplify it:
x^2 = (-23x + 15)/28
Now we can factor the right hand side of the equation. We can do this by finding two numbers, let's say a and b, such that a + b = -23 and ab = 15.
The numbers -5 and -3 fit these conditions since -5 + (-3) = -8 and -5 * -3 = 15.
So, we can rewrite the equation as:
x^2 = (-23x + 15)/28
x^2 = (-5x + 3)(-3x + 5)