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What is the missing constant term in the perfect square that starts with
x^(2)-8x ?

What is the missing constant term in the perfect square that starts with $x^{2}-8x$ ?

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Solve a quadratic equation by completing the square

Full solution

Q. What is the missing constant term in the perfect square that starts with

x^{2}-8x

?

Step $1$ : Identify the expression: To complete the square for an expression of the form $x^2 - bx$ , we need to find the value that makes it a perfect square trinomial. This value is found by taking $(\frac{b}{2})^2$ .
Step $2$ : Calculate the value of $\frac{b}{2}$ : In the expression $x^2 - 8x$ , the coefficient $b$ in front of $x$ is $-8$ . To find the constant term that completes the square, we calculate $\left(-\frac{8}{2}\right)^2$ .
Step $3$ : Square the value: Performing the calculation, we get $(-\frac{8}{2})^2 = (-4)^2 = 16$ .
Step $4$ : Add the constant term to the expression: The missing constant term that completes the square for the expression $x^2 - 8x$ is $16$ . Adding this term to the expression would give us a perfect square trinomial: $x^2 - 8x + 16$ .

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