Solve the Equation: (2x)² - 3 = 6 Step-by-Step

Question

(2x)23=6 (2x)^2-3=6

Video Solution

Solution Steps

00:00 Solve
00:05 Always solve parentheses first
00:10 When there's a power on a product of terms, each term is raised to that power
00:18 Arrange the equation so that 0 is on the right side
00:32 Take out 4 from the parentheses
00:42 Convert 9 to 3 squared and 4 to 2 squared
00:51 A squared fraction raises both numerator and denominator to the square
00:55 Use the shortened multiplication formulas
01:15 Find the two possible solutions
01:33 And this is the solution to the question

Step-by-Step Solution

First we rearrange the equation and set it to 0

4x236=0 4x^2-3-6=0

4x29=0 4x^2-9=0

We then apply the shortcut multiplication formula:

4(x294)=0 4(x^2-\frac{9}{4})=0

x2(32)2=0 x^2-(\frac{3}{2})^2=0

(x32)(x+32)=0 (x-\frac{3}{2})(x+\frac{3}{2})=0

x=±32 x=\pm\frac{3}{2}

Answer

±32 ±\frac{3}{2}