What must be added to x 2 16x ____ to make it a perfect square?
64
Thus, in the given problem x2 + 16x. We have to add 82 = 64, to convert it into a perfect square. Therefore, 64 must be added to the expression to make it a perfect-square trinomial.
What is the factor of x 2 16?
There are two ways to factorize x2−16 – one using identity a2−b2=(a+b)(a−b) . Other method is by splitting the middle term, which is 0 here and as product of coefficient of x2 and constant term is −16 .
What must be added to X 2 X to make it perfect square trinomial?
The value which must be added to the expression x2 + x to make it a perfect square trinomial is 1/4.
How many solutions does x 2 =- 16 have?
two solutions
If we have the equation x2 = 16, what are the solutions to the equation? Since the square of a positive or negative number are always positive, this equation has two solutions, namely x = -4 or x = 4.
How do you complete the square of x 2 12x?
Divide the coefficient of the x -term by 2, then square the result. Add the result to both sides. Factor the perfect square trinomial x2+12x+36 on the left-hand side. Take the square root of both sides and solve for x .
How do you complete the square of x 2 8x?
Arrange the tiles for x2 – 8x so that two sides of the figure are congruent. To make the figure a square, add 16 positive 1-tiles.
What is x2 + 3x = – 1/4?
The coefficient in our case equals 4. Dividing 4 into each member results in x2 + 3x = – 1/4. First we need to find the constant term of our complete square. The coefficient of x, which equals 3 is divided by 2 and squared, giving us 9/4. Then we add and subtract 9/4 as shown above.
How do you solve X2 + 8x + 1 6?
To solve the equation, factor x 2 + 8 x + 1 6 using formula x 2 + ( a + b) x + a b = ( x + a) ( x + b). To find a and b, set up a system to be solved. Since ab is positive, a and b have the same sign.
What is x2 – 8x + 16 as a complete square?
We add and subtract 16 and can see that x2 – 8x + 16 gives us a complete square. Since the constant term -8 is with the minus sign, we use this general form: (x – a)2 = x2 – 2ax + a2. Using our numbers gives us: x2 – 8x + 16 = x2 – 2* (4)*x + (4)2 = (x – 4)2.
How to factor X^2-16 in Algebra?
Algebra. Factor x^2-16. x2 − 16 x 2 – 16. Rewrite 16 16 as 42 4 2. x2 − 42 x 2 – 4 2. Since both terms are perfect squares, factor using the difference of squares formula, a2 −b2 = (a+b)(a−b) a 2 – b 2 = ( a + b) ( a – b) where a = x a = x and b = 4 b = 4.