Rewrite the function by completing the square. {:[g(x)=4x^(2)-28 x+49],[g(x)=◻(x+◻)^(2)+◻]:}

Calculate Rolls Needed: First, let's figure out how many rolls the electrician needs by dividing the total amount of tape needed by the amount of tape on each roll. 8,000 cm ÷ 2,000 cm/roll = 4 rolls.Factor Out Coefficient: We start by factoring out the coefficient of x^2 from the first two terms. g(x) = 4(x^2 - 7x) + 49.Find Completing Square Value: Next, we find the value to complete the square. We take the coefficient of x, divide it by 2, and square it. (-7/2)^2 = 49/4.Add Completing Square: We add and subtract this value inside the parentheses to complete the square. g(x) = 4(x^2 - 7x + 49/4 - 49/4) + 49.Rewrite Function: Now we rewrite the function with the completed square inside the parentheses and adjust the constant term outside. g(x) = 4((x - 7/2)^2 - 49/4) + 49.Simplify Constant Terms: Finally, we simplify the constant terms. g(x) = 4(x - 7/2)^2 - 4(49/4) + 49. g(x) = 4(x - 7/2)^2 - 49 + 49. g(x) = 4(x - 7/2)^2.

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Algebra 1

Powers with decimal and fractional bases

Full solution

Q. Rewrite the function by completing the square.

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\begin{array}{l} g(x)=4 x^{2}-28 x+49 \\ g(x)=\square(x+\square)^{2}+\square \end{array}

Calculate Rolls Needed: First, let's figure out how many rolls the electrician needs by dividing the total amount of tape needed by the amount of tape on each roll. $8,000 \, \text{cm} \div 2,000 \, \text{cm}/\text{roll} = 4 \, \text{rolls}.$
Factor Out Coefficient: We start by factoring out the coefficient of $x^2$ from the first two terms. $\newline$ $g(x) = 4(x^2 - 7x) + 49$ .
Find Completing Square Value: Next, we find the value to complete the square. We take the coefficient of $x$ , divide it by $2$ , and square it. $(-\frac{7}{2})^2 = \frac{49}{4}$ .
Add Completing Square: We add and subtract this value inside the parentheses to complete the square. $\newline$ $g(x) = 4(x^2 - 7x + \frac{49}{4} - \frac{49}{4}) + 49$ .
Rewrite Function: Now we rewrite the function with the completed square inside the parentheses and adjust the constant term outside. $\newline$ $g(x) = 4((x - \frac{7}{2})^2 - \frac{49}{4}) + 49$ .
Simplify Constant Terms: Finally, we simplify the constant terms. $g(x) = 4(x - \frac{7}{2})^2 - 4(\frac{49}{4}) + 49.$ $g(x) = 4(x - \frac{7}{2})^2 - 49 + 49.$ $g(x) = 4(x - \frac{7}{2})^2.$