Solve the following equation to find the value of $x$
$x(4 x+11)-4\left(x^2+7\right)=49$
Answer (1)
Expand the left side of the equation: x ( 4 x + 11 ) − 4 ( x 2 + 7 ) = 4 x 2 + 11 x − 4 x 2 − 28 .
Simplify the equation: 11 x − 28 = 49 .
Isolate x : 11 x = 77 .
Solve for x : x = 11 77 = 7 . The final answer is 7 .
Explanation
Understanding the Problem We are given the equation x ( 4 x + 11 ) − 4 ( x 2 + 7 ) = 49 and we want to find the value of x .
Expanding the Equation First, let's expand the left side of the equation: x ( 4 x + 11 ) − 4 ( x 2 + 7 ) = 4 x 2 + 11 x − 4 x 2 − 28 Notice that 4 x 2 and − 4 x 2 cancel each other out.
Isolating x Now we have: 11 x − 28 = 49 Next, we want to isolate x . Add 28 to both sides of the equation: 11 x = 49 + 28 11 x = 77
Solving for x Finally, divide both sides by 11 to solve for x :
x = 11 77 x = 7
Final Answer Therefore, the value of x is 7.
Examples
Imagine you're trying to figure out how many hours you need to work this week to afford a new video game. If the game costs $49, and you already have a job that pays you $11 per hour but you have to spend $28 on gas to get to work, this equation helps you calculate the number of hours (x) you need to work to afford the game. By solving the equation, you find out exactly how many hours you need to put in to reach your goal.
