Solve each equation using simplification techniques. Round answers to two decimal places as necessary.

$21-(-17 P)(20 P)=392$

Simplify the equation: 21 + 340 P 2 = 392 .
Isolate the term with P 2 : 340 P 2 = 371 .
Solve for P : P = ± 340 371 ​ ​ .
Round to two decimal places: P = ± 1.04 . The solutions are P = 1.04 , − 1.04 ​ .

Explanation

Problem Analysis We are given the equation 21 − ( − 17 P ) ( 20 P ) = 392 and we need to solve for P , rounding the answers to two decimal places.

Simplifying the Equation First, let's simplify the equation by expanding the product: 21 − ( − 17 P ) ( 20 P ) = 392 . This simplifies to 21 + 340 P 2 = 392 .

Isolating the Term with P^2 Next, we subtract 21 from both sides of the equation: 340 P 2 = 392 − 21 , which gives 340 P 2 = 371 .

Isolating P^2 Now, we divide both sides by 340 to isolate P 2 : P 2 = 340 371 ​ .

Taking the Square Root To solve for P , we take the square root of both sides: P = ± 340 371 ​ ​ . This gives us two possible solutions for P .

Calculating the Values of P We calculate the two possible values of P : P = 340 371 ​ ​ and P = − 340 371 ​ ​ . Using a calculator, we find that P ≈ 1.04459 and P ≈ − 1.04459 .

Rounding to Two Decimal Places Finally, we round the values to two decimal places: P ≈ 1.04 and P ≈ − 1.04 . Therefore, the solutions are P = 1.04 and P = − 1.04 .


Examples
Understanding quadratic equations is crucial in various fields, such as physics and engineering. For instance, when designing a bridge, engineers use quadratic equations to model the parabolic shape of the bridge's arch. By solving these equations, they can determine the optimal dimensions and ensure the bridge's structural integrity. Similarly, in physics, projectile motion can be described using quadratic equations, allowing us to predict the trajectory of an object, like a ball thrown in the air.

Answered by GinnyAnswer | 2025-07-08