X2-21x+84=0 that's xsquared (x- ? )(x- ? )
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x^2-21x+84=0
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To find the values of "x" that satisfy the equation x^2 - 21x + 84 = 0 and factorize it, you can use the quadratic formula or the method of factoring by grouping.
Using the quadratic formula, which states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation x^2 - 21x + 84 = 0, we can directly compare the coefficients to find a = 1, b = -21, and c = 84. Substituting these values in the quadratic formula, the equation becomes:
x = (-(-21) ± √((-21)^2 - 4*1*84)) / (2*1)
= (21 ± √(441 - 336)) / 2
= (21 ± √105) / 2
Hence, the two possible solutions for "x" are:
x = (21 + √105) / 2
x = (21 - √105) / 2
To factorize the quadratic equation x^2 - 21x + 84 = 0, you need to express it as a product of two binomials in the form (x - ?)(x - ?), where you find the values that fill in the blanks.
One way to factorize it is by using trial and error. Identify two numbers whose product is equal to the constant term (84) and whose sum is equal to the coefficient of the middle term (-21). In this case, the numbers are 6 and 14 (-6 * -14 = 84 and 6 + 14 = -21).
Thus, the factorized form of the equation is:
(x - 6)(x - 14)
By setting each binomial to zero, you can find the possible values of "x":
x - 6 = 0 --> x = 6
x - 14 = 0 --> x = 14
Therefore, the factorized form of x^2 - 21x + 84 = 0 is (x - 6)(x - 14), and the possible values for "x" are 6 and 14.