Answer:
[tex]x=-\dfrac{3}{2}, x=\dfrac{7}{2}[/tex]
Step-by-step explanation:
Let the unknown number = x
[tex]\implies 4x^2=21+8x[/tex]
[tex]\implies 4x^2-8x-21=0[/tex]
Factor the equation
Find factors of -84 that sum to -8: -14 and 6
Rewrite -8x as the sum of these 2 numbers:
[tex]\implies 4x^2-14x+6x-21=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 2x(2x-7)+3(2x-7)=0[/tex]
Factor out the common term [tex](2x-7)[/tex]:
[tex]\implies (2x+3)(2x-7)=0[/tex]
Therefore,
[tex]\implies 2x+3=0 \implies x=-\dfrac{3}{2}[/tex]
[tex]\implies 2x-7=0 \implies x=\dfrac{7}{2}[/tex]
