Maya is solving the quadratic equation by completing the square. 4x2 + 16x + 3 = 0 What should Maya do fir

Question

Maya is solving the quadratic equation by completing the square.

4×2 + 16x + 3 = 0

What should Maya do first?

Isolate the variable x2.
Subtract 16x from both sides of the equation.
Isolate the constant.
Factor 4 out of the variable terms.

Sapo1 · Answer

Answer:   Isolate the constant.     Step-by-step explanation:        Given quadratic equation :  4x^2+16x+3=0     Completing the Square    Step 1    Isolate the constant  by subtracting 3 from both sides:   implies 4x^2+16x+3-3=0-3   implies 4x^2+16x=-3     Step 2     Factor out the coefficient of x²  from the left side:   implies 4(x^2+4x)=-3  Divide both sides by 4:   implies x^2+4x=- dfrac{3}{4}     Step 3    Add the square of half the coefficient of x  to both sides.  This forms a  perfect square trinomial  on the left side:   implies x^2+4x+ left( dfrac{4}{2} right)^2=- dfrac{3}{4}+ left( dfrac{4}{2} right)^2  Simplify:   implies x^2+4x+4=- dfrac{3}{4}+4   implies x^2+4x+4= dfrac{13}{4}     Step 4    Factor the perfect square trinomial  on the left side:   implies (x+2)^2= dfrac{13}{4}  We have now  completed the square .       To solve , square root both sides:   implies  sqrt{(x+2)^2}= sqrt{ dfrac{13}{4}}   implies x+2= pm sqrt{ dfrac{13}{4}}   implies x+2= pm dfrac{ sqrt{13}}{ sqrt{4}}   implies x+2= pm dfrac{ sqrt{13}}{2}    Subtract 2 from both sides:   implies x+2-2=-2 pm dfrac{ sqrt{13}}{2}   implies x=-2 pm dfrac{ sqrt{13}}{2}    Rewrite -2 as -4/2:   implies x=- dfrac{4}{2} pm dfrac{ sqrt{13}}{2}   textsf{Apply the fraction rule} quad  dfrac{a}{c}  pm  dfrac{b}{c}= dfrac{a  pm b}{c}:   implies x= dfrac{-4  pm sqrt{13}}{2}    Learn more about  completing the square  here:  https://brainly.com/question/27933930  https://brainly.com/question/27591531

mocmien2 · Answer

Step-by-step explanation:   factor 4 out of the variable terms, as this helps.     but my approach is simply to define the target and then calculate 'backwards'.  we want to find  (ax + b)² = a²x² + 2abx + b²  and now we compare with the original equation :  a²x² = 4x²  a² = 4  a = 2    2abx = 16x  2×2×bx = 16x  4b = 16  b = 4    b² = 16, but we have only 3, so we need to subtract 16-3 = 13 from the completed square.    so, our equation is  (2x + 4)² - 13 = 0  (2x + 4)² = 13  2x + 4 = sqrt(13)  2x = sqrt(13) - 4  x = sqrt(13)/2 - 2

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