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Solve the quadratic equation to find the value of ‘x’ $2{{\text{x}}^2} - 7 = 0$.

Last updated date: 13th Jul 2024
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Hint:- Compare the given equation with standard quadratic equation and use the quadratic formula to solve the equation.

Given, $2{{\text{x}}^2} - 7 = 0$. We need to find the value of x which satisfies the given equation.
A general form of quadratic equation is ${\text{a}}{{\text{x}}^2} + {\text{ bx + c = 0}}$. Comparing the given equation from the general form we can easily conclude that the given equation is a quadratic equation.
A general quadratic equation in one variable can be solved by using the quadratic formula. i.e.
$\dfrac{{ - {\text{b}} \pm \sqrt {{{\text{b}}^2} - 4{\text{ac}}} }}{{2{\text{a}}}}$.
Now comparing the coefficients of $2{{\text{x}}^2} - 7 = 0$ with the general form of quadratic equation , we get
a = 2 , b= 0 and c = -7.
Now, applying the quadratic formula for $2{{\text{x}}^2} - 7 = 0$
x =$\dfrac{{ - {\text{b}} \pm \sqrt {{{\text{b}}^2} - 4{\text{ac}}} }}{{2{\text{a}}}}$
x = $\dfrac{{ - 0 \pm \sqrt {{0^2} - 4 \times 2 \times \left( { - 7} \right)} }}{{2 \times 2}}$
x = $\dfrac{{ \pm \sqrt {56} }}{4}$
x = $\dfrac{{ \pm 2\sqrt {14} }}{4}$
x = $\dfrac{{ \pm \sqrt {14} }}{2}$
Hence, the value of x that satisfies the given equation is $\dfrac{{ \pm \sqrt {14} }}{2}$.

Note:- In these types of questions, the key concept is to check the degree of the equation. If it is a linear equation then only by simplifying the equation we can find the unknown. But if the equation is quadratic i.e. the degree of equation is 2, then the quadratic formula needs to be applied.