Question

(4x+3)•(x-12)-39x=7 розв'язання рівняння

Answer 1

$\displaystyle \tt (4x+3)(x-12)-39x=7\\\displaystyle \tt 4x^2-48x+3x-36-39x=7\\\displaystyle \tt 4x^2-84x-36=7\\\displaystyle \tt 4x^2-84x-36-7=0\\\displaystyle \tt 4x^2-84x-43=0\\\displaystyle \tt 2x(2x+1)-43(2x+1)=0\\\displaystyle \tt (2x+1)(2x-43)=0\\\\ \displaystyle \tt 2x+1=0\\\displaystyle \tt 2x=-1\\\displaystyle \tt x=-1\div2\\\displaystyle \tt \bold{x_1=-0,5}\\\\ \displaystyle \tt 2x-43=0\\\displaystyle \tt 2x=43\\\displaystyle \tt x=43\div2\\\displaystyle \tt \bold{x_2=21,5}$

Answer 2

To solve the equation (4x+3) • (x-12) - 39x = 7, we'll follow these steps:

Step 1: Expand the brackets. Step 2: Simplify the equation. Step 3: Move all the x terms to one side and the constant terms to the other side. Step 4: Factorize the quadratic equation. Step 5: Solve for x.

Let's go through each step:

Step 1: Expand the brackets: (4x + 3) • (x - 12) = 4x² - 48x + 3x - 36 = 4x² - 45x - 36

Step 2: Simplify the equation: 4x² - 45x - 36 - 39x = 7

Step 3: Move all the x terms to one side and the constant terms to the other side: 4x² - 45x - 39x - 36 - 7 = 0 4x² - 84x - 43 = 0

Step 4: Factorize the quadratic equation: To factorize, we look for two numbers that multiply to give the product of the coefficient of x² (4) and the constant term (-43) and add up to the coefficient of the x term (-84). The two numbers are -86 and 1 (-86 + 1 = -85, close to -84).

4x² - 86x + x - 43 = 0

Step 5: Factor by grouping: (4x² - 86x) + (x - 43) = 0 2x(2x - 43) + (2x - 43) = 0 (2x + 1)(2x - 43) = 0

Now, set each factor to zero and solve for x:

1. 2x + 1 = 0 2x = -1 x = -1/2

2. 2x - 43 = 0 2x = 43 x = 43/2

So, the solutions to the equation are x = -1/2 and x = 43/2.