Transform each of the following equations into aquadratic equation in the form ax² + bx + c = 0.1) x (x+5)= 222.) (s+6)=153.) 2 - 34₤ - 341 = 174) 1 - 1/2 = 1/365.) x(x+3)=28gave the answer and solution ​

Step-by-step explanation:Let's break down each of these into a quadratic equation in the form \(ax^2 + bx + c = 0\). I'll guide you through each step like we're solving it together. 1) \(x(x + 5) = 2\)Solution:1. First, distribute \(x\) to both terms inside the parentheses: \[ x^2 + 5x = 2 \]2. To make it a standard quadratic equation, move the 2 to the left side by subtracting 2 from both sides: \[ x^2 + 5x - 2 = 0 \]Answer: \(x^2 + 5x - 2 = 0\)---### 2) \((s + 6) = 15\)Solution:1. Move the 15 to the left side by subtracting it from both sides: \[ s + 6 - 15 = 0 \]2. Simplify: \[ s - 9 = 0 \] This is a linear equation, not quadratic.Answer: \(s - 9 = 0\) (This is not a quadratic equation; it's linear.)---3) \(2 \cdot \frac{3s}{4} - \frac{34s}{1} = 1\)Solution:1. First, simplify the terms. Multiply \(2\) by \(\frac{3s}{4}\): \[ \frac{6s}{4} - 34s = 1 \] Simplify \(\frac{6s}{4}\) to \(\frac{3s}{2}\): \[ \frac{3s}{2} - 34s = 1 \]2. Clear the fraction by multiplying everything by 2: \[ 3s - 68s = 2 \]3. Combine like terms: \[ -65s = 2 \] This simplifies to a linear equation, not quadratic.Answer: \(-65s = 2\) (This is also linear.)--- 4) \(\frac{1}{6} - \frac{1}{2} = \frac{1}{3}\)Solution:1. Clear the fractions by finding a common denominator. Multiply everything by 6: \[ 1 - 3 = 2 \] Simplify: \[ -2 = 2 \] This equation simplifies further but is not quadratic.Answer: \(-2 = 2\) (This is not a valid equation; it simplifies to a contradiction.)--- 5) \(x(x + 3) = 28\)Solution:1. Distribute \(x\) to both terms inside the parentheses: \[ x^2 + 3x = 28 \]2. Move the 28 to the left side by subtracting it from both sides: \[ x^2 + 3x - 28 = 0 \]Answer: \(x^2 + 3x - 28 = 0\)---

Answered by edelyntoyogonviola | 2024-09-09