Solve (1.4+x)(1.4-x)=(x-1.7)(7.6-x)

$$( 1.4 + x ) ( 1.4 - x ) = ( x - 1.7 ) ( 7.6 - x )$$

Solve for x

$$x=1.6$$

Steps for Solving Linear Equation

Consider \left(1.4+x\right)\left(1.4-x\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 1.4.

$$1.96-x^{2}=\left(x-1.7\right)\left(7.6-x\right)$$

Use the distributive property to multiply x-1.7 by 7.6-x and combine like terms.

$$1.96-x^{2}=9.3x-x^{2}-12.92$$

Subtract 9.3x from both sides.

$$1.96-x^{2}-9.3x=-x^{2}-12.92$$

Add x^{2} to both sides.

$$1.96-x^{2}-9.3x+x^{2}=-12.92$$

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

$$1.96-9.3x=-12.92$$

Subtract 1.96 from both sides.

$$-9.3x=-12.92-1.96$$

Subtract 1.96 from -12.92 to get -14.88.

$$-9.3x=-14.88$$

Divide both sides by -9.3.

$$x=\frac{-14.88}{-9.3}$$

Expand \frac{-14.88}{-9.3} by multiplying both numerator and the denominator by 100.

$$x=\frac{-1488}{-930}$$

Reduce the fraction \frac{-1488}{-930} to lowest terms by extracting and canceling out -186.

$$x=\frac{8}{5}$$