help me find the exact solutions for this equation. explain step by step how you got your answer. i will provide an example of what’s expected in the second photo attached. **Show What You Know: Solving Equations with Various Function Types****MAT 190 - Precalculus**---**Objectives:**The purpose of this assignment is for you to:1. Demonstrate your ability to solve equations with various function types;2. Improve your mathematical writing to include full solutions with justifications;3. Integrate mathematical statements into grammatically correct expositions.---**Assignment:**Find all exact solutions to the following equation:\[ 2e^{x^2} - 3(3x + 5) \cos(x^3 + 1) = 0 \]Include a detailed explanation for each mathematical step written in grammatically correct, complete sentences within a 2-column format. ---## Solving the Equation: Step-by-Step Explanation### Problem Statement:\[ 5e^{\cos(x^2)}(-\sin(x^2))(3x^2) = 0 \]>This is the equation we were given to solve.### Step 1: Simplifying the Equation\[ -15x^2 e^{\cos(x^2)} \sin(x^2) = 0 \]**Explanation:**1. We began by cleaning up the expression on the left side of the equation.2. Using the commutative and associative properties of multiplication, we pulled the negative sign to the front and completed the multiplication of the 5 and the \(3x^2\) to get the first factor of \(-15x^2\).3. We left the other two factors alone since there was not anything we could do to simplify them.4. Now that the left side of the equation is as simplified as possible and is in factored form, we are ready to continue.### Step 2: Applying the Zero Product Property\[ -15x^2 = 0 \quad e^{\cos(x^2)} = 0 \quad \sin(x^2) = 0 \]**Explanation:**Using the zero product property, we set each factor on the left side of the equation equal to zero to solve the equation.### Step 3: Solving the Simpler Equations#### \(\mathbf{-15x^2 = 0}\)\[ -15x^2 = 0 \]\[ x^2 = 0 \]\[ x = 0 \]**Explanation:**We solved the first equation by first dividing both sides by \(-15\) and then taking the square root of both sides of the equation, paying attention to include both the positive and negative root. However, in this particular case, \( x^2 = 0 \) implies:\[ x = 0 \]---This step-by-step breakdown guides the learner through the process of simplifying a given complex equation by using properties of multiplication and solving the resulting simpler equations through the zero product property.

Answered: Image /qna-images/answer/4fdb42da-865c-40eb-beb7-ffbc3b8a1907.jpg

Answered: Assignment: Find all exact solutions to…

Assignment: Find all exact solutions to the following equations: 2e ³(3x+5) cos(x³ + 1) = 0

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter5: Linear Inequalities

Section: Chapter Questions

Problem 6SGR

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