Express the following in completed square form:
y = (2x)^2 + 14x - 11
Please show the work because I do not understand it.
recall that a^2+2ab+b^2 = (a+b)^2
(2x)^2 + 14x - 11
4x^2 + 14x - 11
4(x^2 + 7/2) - 11
4(x^2 + 7/2 + (7/4)^2) - 11 - 4(49/16)
4(x + 7/4)^2 - 44/4 - 49/4
4(x + 7/4)^2 - 93/4
The answer in the book says:
y = 2 (x+7/2)^2 -71/2
(2x)^2 + 14x - 11
checking if x=1, value is 4+14-11=7
checking book answer, if x=1, 2(9/2)^2-71/2=10
checking oobleck's answer: if x=1, y=4(1+7/4)^2-93/4=121/4-93/4=128/4=7
book answer is wrong.
To express the given quadratic equation, y = (2x)^2 + 14x - 11, in completed square form, follow these steps:
Step 1: Group the first two terms.
y = (4x^2) + 14x - 11
Step 2: Take half of the coefficient of the x-term, square it, and add it to both sides of the equation.
y + (7)^2 = (4x^2) + 14x + (7)^2
Step 3: Simplify the right side by factoring a perfect square trinomial.
y + 49 = (2x + 7)^2
Therefore, the equation y = (2x)^2 + 14x - 11, expressed in completed square form, is:
y + 49 = (2x + 7)^2