Solve If 49x ^ 2 - b = (7x + 1/2)(7x - 1/2) then the value of b is : | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$49 x ^ { 2 } - b = ( 7 x + \frac { 1 } { 2 } ) ( 7 x - \frac { 1 } { 2 } ) , b$$

Solve for b

$b=\frac{1}{4}=0.25$

Steps for Solving Linear Equation

Consider $\left(7x+\frac{1}{2}\right)\left(7x-\frac{1}{2}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$. Square $\frac{1}{2}$.

$$49x^{2}-b=\left(7x\right)^{2}-\frac{1}{4}$$

Expand $\left(7x\right)^{2}$.

$$49x^{2}-b=7^{2}x^{2}-\frac{1}{4}$$

Calculate $7$ to the power of $2$ and get $49$.

$$49x^{2}-b=49x^{2}-\frac{1}{4}$$

Subtract $49x^{2}$ from both sides.

$$-b=49x^{2}-\frac{1}{4}-49x^{2}$$

Combine $49x^{2}$ and $-49x^{2}$ to get $0$.

$$-b=-\frac{1}{4}$$

Multiply both sides by $-1$.

$$b=\frac{1}{4}$$

Solve for x (complex solution)

$x\in \mathrm{C}$
$b = \frac{1}{4} = 0.25$

Solve for x

$x\in \mathrm{R}$
$b = \frac{1}{4} = 0.25$