dimitri is solving the equation ( x^{2}-10x = 21 ). which value must be added to both sides of the equation…
dimitri is solving the equation ( x^{2}-10x = 21 ). which value must be added to both sides of the equation to make the left side a perfect - square trinomial?\n0\n4\n25\n100
Answer
Explanation:
Step1: Recall the formula for a perfect - square trinomial
For a quadratic expression of the form (x^{2}+bx), the value to be added to make it a perfect - square trinomial is ((\frac{b}{2})^{2}). In the given equation (x^{2}-10x = 21), here (b=- 10).
Step2: Calculate the value
Substitute (b = - 10) into the formula ((\frac{b}{2})^{2}). We have ((\frac{-10}{2})^{2}=(-5)^{2}=25).
Answer:
25