Question

$4x ^{2} - 35x - 9$
​

Answer 1

Refer to the attachment

Hope it helps you out......

Answer 2

Answer:

$\boxed{\sf x = 9 \ \ or \ \ x = -\frac{1}{4}}$

Step-by-step explanation:

$\sf Solve \: for \: x \: over \: the \: real \: numbers: \\ \sf \implies 4 {x}^{2} - 35x - 9 = 0 \\ \\ \sf The \: left \: hand \: side \: factors \: into \: a \: product \: with \: two \: terms: \\ \sf \implies 4 {x}^{2} - (36 - 1)x - 9 = 0 \\ \\ \sf \implies 4 {x}^{2} - 36x + x - 9 = 0 \\ \\ \sf \implies 4x(x - 9) + 1(x - 9) = 0 \\ \\ \sf \implies(x - 9)(4x + 1) = 0 \\ \\ \sf Split \: into \: two \: equations: \\ \sf \implies x - 9 = 0 \: \: \: \: or \: \: \: \: 4x + 1 = 0 \\ \\ \sf Add \: 9 \: to \: both \: sides: \\ \sf \implies \boxed{ \sf x = 9} \: \: \: \: or \: \: \: \:4x + 1 = 0 \\ \\ \sf Subtract \: 1 \: from \: both \: sides: \\ \sf \implies x = 9 \: \: \: \: or \: \: \: \: \boxed{ \sf 4x = - 1} \\ \\ \sf Divide \: both \: sides \: by \: 4: \\ \sf \implies x = 9 \: \: \: \: or \: \: \: \: \boxed{ \sf x = - \frac{1}{4} }$