Question

i need help to solve this quadratic formula i need a full solution thats all
1. X^2+5x-14 ​
2. 2x^2+8x-10=0
3.2x^2+3x=27

Answer 1

$\huge{\underline{\bf\red{Questi {\mathbb{O}} n} :}}$

Solve the quadratic equations :-

• $\boxed{ {x}^{2} + 5x - 14 = 0 }$

• $\boxed{2 {x}^{2} + 8x - 10 = 0 }$

• $\boxed{2 {x}^{2} + 3x - 27 = 0 }$

$\huge{\underline{\bf{\color{lightgreen}{Soluti {\mathbb{O}} n}}\ :}}$

$\underline{ \underline{ \bf \blue{option} \ \red{(i)}}}$

$\begin{aligned} \\ \qquad {x}^{2} + 5x - 14 & = 0 \\ \\ \implies \ \ {x}^{2} + (7 - 2)x - 14 & = 0 \\ \\ \implies \ \ \: {x}^{2} + 7x - 2x - 14 & = 0 \\ \\ \implies x(x + 7) - 2(x + 7) & = 0 \\ \\ \implies \qquad \ (x + 7)(x - 2) & = 0 \\ \\ \implies(x + 7) = 0 \quad \boxed{or} \quad &(x - 2) = 0 \\ \\ \implies x = - 7 \qquad \ \ \ \boxed{or} \quad& x = 2& & & \end{aligned}$

$\underline{ \underline{ \bf \blue{option} \ \red{(ii)}}}$

$\begin{aligned} \\ \qquad 2{x}^{2} + 8x - 10 & = 0 \\ \\ \implies \qquad \quad \ \ {x}^{2} + 4x - 5& = 0 \\ \\ \implies \quad {x}^{2} + (5 - 1)x - 5 & = 0 \\ \\ \implies \quad \ \ \ {x}^{2} + 5x - x - 5 & = 0 \\ \\ \implies x(x + 5) - 1(x + 5) & = 0 \\ \\ \implies \qquad \ (x + 5)(x - 1) & = 0 \\ \\ \implies(x + 5) = 0 \quad \boxed{or} \quad &(x - 1) = 0 \\ \\ \implies x = - 5 \qquad \ \ \ \boxed{or} \quad& x = 1& & & \end{aligned}$

$\underline{ \underline{ \bf \blue{option} \ \red{(iii)}}}$

$\begin{aligned} \\ \qquad 2{x}^{2} + 3x - 27 & = 0 \\ \\ \implies \quad 2{x}^{2} + (9 - 6)x - 27 & = 0 \\ \\ \implies \quad \: 2 {x}^{2} + 9x - 6x - 27 & = 0 \\ \\ \implies x(2x + 9) - 3(2x + 9) & = 0 \\ \\ \implies \qquad \ \ \ (2x + 9)(x - 3) & = 0 \\ \\ \implies \ \ (2x + 9) = 0 \quad \boxed{or} \quad &(x - 3) = 0 \\ \\ \implies \ \ \ x = - \frac{9}{2} \qquad \ \ \ \boxed{or} \quad& x = 3& & & \end{aligned}$

$\red{\rule{5.5cm}{0.02cm}}$

Method Used :-

$\boxed{ \bf \quad Middle \quad Term \quad Splitting \quad }$

$\purple{\rule{7.5cm}{0.02cm}}$

$\Large{ \mid {\underline{\underline{\bf\green{BrainLiest \ AnswEr}}}} \mid }$

Answer 2

$\fbox\purple{A}\fbox\red{N}\fbox\green{S}\fbox\orange{W}\fbox\pink{E}\fbox\purple{R}$

1

• $x = - 7 \quad \boxed{or} \quad x = 2$

2

• $x = - 5 \quad \boxed{or} \quad x = 1$

3

• $x = - \dfrac{9}{2} \quad \boxed{or} \quad x = 3$

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${\fcolorbox{white}{lightgreen}{{\footnotesize{{ \: \color{white}{\checkmark} }}} \ {\small{ \sf Verified \: answer}}}}$

${\fcolorbox{white}{yellow}{{\footnotesize{{ • {{}^{ {•}}}•\!\!\!\!\!\Delta\!\!\!\neg \!\!\!\!\llcorner \!\!\!\!- }}} {\small{ \sf Brainliest \: answer}}}}$