Question

(2x-1)(x+4)-2x^2+4/2x-4=6

solve the following equation and find the value of x​

Answer 1

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow (2x-1)(x+4)-2x^2+ \dfrac{4}{2} x -4=6$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow VALUE\:OF\:X$

$\large\underline\bold{SOLUTION,,}$

$\sf\therefore (2x-1)(x+4)-2x^2+ \dfrac{4}{2} x -4=6$

$\sf\implies (2x-1)(x+4)-2x^2+ \dfrac{4}{2} x -4=6$

$\sf\implies 2x^2+8x-x-4-2x^2 +\cancel \dfrac{4}{2} x -4=6$

$\sf\implies 2x^2+8x-x-4-2x^2+2x-4=6$

$\sf\implies 2x^2-2x^2+8x-x+2x-4-4=6$

$\sf\implies \cancel{2x^2}-\cancel{2x^2}+8x-x+2x-4-4=6$

$\sf\implies 7x+2x-8=6$

$\sf\implies 9x-8=6$

$\sf\implies 9x=6+8$

$\sf\implies 9x= 14$

$\sf\implies x= \dfrac{14}{9}$

$\large{\boxed{\bf{ \star\:\: x=\dfrac{14}{9}\:\: \star}}}$

$\large\underline\bold{VALUE\:OF\:X\:IS\: \dfrac{14}{9}}$

__________________

Answer 2

Question

Solve the following equation and find the value of x​ ⇒ $(2x-1)(x+4)-2x^{2}+\frac{4}{2x}-4 = 6$

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Answer

Let's solve your equation step-by-step.

⇒ $(2x-1)(x+4)-2x^{2}+\frac{4}{2x}-4 = 6$

⇒ $\frac{14x^{2}-16x+4}{2x} =6$

Step 1: Multiply both sides by x.

⇒ $7x^{2}-8x+2=6x$

(Subtract 6x from both sides)

⇒ $7x^{2}-8x+2-6x=6x-6x$

⇒ $7x^{2}-14x+2=0$

For this equation: a = 7, b = -14, c = 2

⇒ $7x^{2}+-14x+2=0$

(Use quadratic formula with a = 7, b = -14, c = 2)

⇒ $x= \frac{-b\± \sqrt{b^{2}-4ac} }{2a}$

⇒ $x= \frac{-(-14)\± \sqrt{-14^{2}-4(7)(2)} }{2(7)}$

⇒ $x= \frac{14\± \sqrt{196-4(7)(2)} }{2(7)}$

⇒ $x= \frac{14\± \sqrt{196-4(14)} }{2(7)}$

⇒ $x= \frac{14\± \sqrt{196-4\times 14} }{2(7)}$

⇒ $x= \frac{14\± \sqrt{196-56} }{2(7)}$

⇒ $x= \frac{14\± \sqrt{140} }{2\times 7 }$

⇒ $x= \frac{14\± \sqrt{140} }{14}$

⇒ $x = 1+\frac{1}{7} \sqrt{35} \ or \ x = 1+\frac{-1}{7}\sqrt{35}$

$\bf \therefore x = 1+\frac{1}{7} \sqrt{35} \ or \ x = 1+\frac{-1}{7}\sqrt{35} \ in \ the \ equation \ => (2x-1)(x+4)-2x^{2}+\frac{4}{2x}-4 = 6$

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Additional Information

What is an equation?

A mathematical statement that contains an equal sign is known as an equation. There are five types of equations. They are ⇒

• Quadratic Equation.
• Linear Equation.
• Radical Equation.
• Exponential Equation.
• Rational Equation.

What is a quadratic equation?

An equation which has the highest exponent or power of the variable as square.

What is the quadratic formula?

The quadratic formula is ⇒ $\sf \dfrac{-b\± \sqrt{b^{2}-4ac} }{2a}$

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