Question

-(2x+3)^2+(x+5)(2x+5)=16

Answer 1

Объяснение:

–(2x+3)²+(x+5)(2x+5)=16

–(4х²+12х+9)+(2х²+5х+10х+25)=16

–4х²–12х–9+2х²+5х+10х+25=16

–2х²+3х+16=16

–2х²+3х=0

а=–2;

b=3

с=0

Д= 3²–4*(–2)*0= 9–0= 9

х(1)= $\frac{ - 3 + \sqrt{9} }{ - 4} = \frac{ - 3 + 3}{ - 4} = 0$

х(2)= $\frac{ - 3 - \sqrt{9} }{ - 4} = \frac{ - 3 - 3}{ - 4} = \frac{ - 6}{- 4} = \frac{3}{2} = 1.5$

Answer 2

To solve the equation -(2x+3)^2 + (x+5)(2x+5) = 16, we'll follow these steps:

Step 1: Expand the expressions on the left-hand side. Step 2: Combine like terms. Step 3: Move all terms to one side of the equation to set it equal to zero. Step 4: Factor the resulting quadratic equation. Step 5: Solve for 'x'.

Let's start:

Step 1: Expand the expressions on the left-hand side. -(2x+3)^2 + (x+5)(2x+5) = 16

Expanding the first term: -(2x + 3)^2 = -(2x + 3)(2x + 3) = -(4x^2 + 12x + 9) = -4x^2 - 12x - 9

Expanding the second term: (x + 5)(2x + 5) = 2x^2 + 5x + 10x + 25 = 2x^2 + 15x + 25

Step 2: Combine like terms. Now the equation becomes: -4x^2 - 12x - 9 + 2x^2 + 15x + 25 = 16

Step 3: Move all terms to one side of the equation to set it equal to zero. -4x^2 - 12x - 9 + 2x^2 + 15x + 25 - 16 = 0

Step 4: Simplify. -2x^2 + 3x + 0 = 0

Step 5: Factor the quadratic equation. To solve this quadratic equation, we can factor it: -2x^2 + 3x = 0 x(-2x + 3) = 0

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

1. x = 0
2. -2x + 3 = 0 -2x = -3 x = -3 / -2 x = 3/2 or 1.5

So, the solutions to the equation are x = 0 and x = 1.5.