The value should be placed in the blank space is 9 to make the perfect square option (B) 81 is correct.
What is a quadratic equation?
Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
It is given that:
The quadratic equation:
x² - 18x + _ = 4 + _
As we know,
(a - b)² = a² - 2ab + b²
x² - 2(9)(x) + _ = 4 + _
To make the above quadratic equation a perfect square plug 9 in the blank space:
x² - 2(9)(x) + 81 = 4 + 81
x² - 2(9)(x) + 9² = 4 + 9²
(x - 9)² = 4 + 81
(x - 9)² = 85
Thus, the value should be placed in the blank space is 9 to make the perfect square option (B) 81 is correct.
Learn more about quadratic equations here:
brainly.com/question/2263981
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