Algebra one. I don't know how to do!
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The quadratic formula is the general solution for all quadratic equations.
For an equation of the form ax² + bx + c = 0, there are two values of x that satisfy the equation; the x-values are called the roots of the equation.
By using the technique of "completing the square", we find:
x = ( -b ± √(b² - 4·a·c) ) / (2·a).
By substituting the values of a, b, and c, the two values of x are found.
One of the x-values is ( -b + √(b² - 4·a·c) ) / (2·a); the other is
( -b - √(b² - 4·a·c) ) / (2·a).
If 2x² + 2x - 99 is set up as a quadratic equation in the usual form: 2x² + 2x - 99 = 0, then you can apply the quadratic formula to find its roots.
a = 2; b = 2; c = -99, so
x = ( -2 ± √(2² - 4·2·(-99)) ) / (2·2)
= ( -2 ± √(4 - (-792)) ) / 4
= (-2 ± √796) / 4
= (-2 ± 2√199) / 4
= (-1 ± √199) / 2.
The two roots are x = (-1 + √199) / 2 and x = (-1 - √199) / 2.
So, if x = (-1 + √199) / 2 , then x - ((-1 + √199) / 2) = 0;
and if x = (-1 - √199) / 2, then x - ((-1 - √199) / 2) = 0.
These forms, where you have (x+something) or (x-something), are the factors of the original expression.
You can then write 2x² + 2x - 99 = (x - ((-1 + √199) / 2))·(x - ((-1 - √199) / 2)).
For an equation of the form ax² + bx + c = 0, there are two values of x that satisfy the equation; the x-values are called the roots of the equation.
By using the technique of "completing the square", we find:
x = ( -b ± √(b² - 4·a·c) ) / (2·a).
By substituting the values of a, b, and c, the two values of x are found.
One of the x-values is ( -b + √(b² - 4·a·c) ) / (2·a); the other is
( -b - √(b² - 4·a·c) ) / (2·a).
If 2x² + 2x - 99 is set up as a quadratic equation in the usual form: 2x² + 2x - 99 = 0, then you can apply the quadratic formula to find its roots.
a = 2; b = 2; c = -99, so
x = ( -2 ± √(2² - 4·2·(-99)) ) / (2·2)
= ( -2 ± √(4 - (-792)) ) / 4
= (-2 ± √796) / 4
= (-2 ± 2√199) / 4
= (-1 ± √199) / 2.
The two roots are x = (-1 + √199) / 2 and x = (-1 - √199) / 2.
So, if x = (-1 + √199) / 2 , then x - ((-1 + √199) / 2) = 0;
and if x = (-1 - √199) / 2, then x - ((-1 - √199) / 2) = 0.
These forms, where you have (x+something) or (x-something), are the factors of the original expression.
You can then write 2x² + 2x - 99 = (x - ((-1 + √199) / 2))·(x - ((-1 - √199) / 2)).
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there is no factor in this equation.
you can answer it by quadratic formula.
you can answer it by quadratic formula.