Question

1) -12x+4=-9x²2) 13x+3x²=-143) x²-3x=04) 17a²=33-16a

Answer 1

1) х=0.6
2) х1= -2,3 х2= -2

Answer 2

Let's solve each equation step by step:

1. -12x + 4 = -9x²

To solve this equation, we'll rearrange it to the form of a quadratic equation and set it equal to zero:

-9x² + 12x + 4 = 0

Now we can either factor the quadratic equation or use the quadratic formula to find the solutions. Let's use the quadratic formula:

The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions are given by:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = -9, b = 12, and c = 4. Substituting these values into the formula, we get:

x = (-12 ± √(12² - 4(-9)(4))) / (2(-9)) x = (-12 ± √(144 + 144)) / (-18) x = (-12 ± √(288)) / (-18) x = (-12 ± √(144 * 2)) / (-18) x = (-12 ± 12√2) / (-18)

Simplifying further:

x = (6 ± 6√2) / 9 x = 2/3 ± 2/3√2

So the solutions to the equation are x = 2/3 + 2/3√2 and x = 2/3 - 2/3√2.

2. 13x + 3x² = -14

To solve this equation, we'll rearrange it to the form of a quadratic equation and set it equal to zero:

3x² + 13x + 14 = 0

Now we can factor the quadratic equation or use the quadratic formula. Let's factor the equation:

(3x + 2)(x + 7) = 0

Setting each factor equal to zero, we get:

3x + 2 = 0 or x + 7 = 0

Solving these equations, we find:

3x = -2 or x = -7

x = -2/3 or x = -7

So the solutions to the equation are x = -2/3 and x = -7.

3. x² - 3x = 0

To solve this equation, we'll factor out x:

x(x - 3) = 0

Setting each factor equal to zero, we get:

x = 0 or x - 3 = 0

Solving these equations, we find:

x = 0 or x = 3

So the solutions to the equation are x = 0 and x = 3.

4. 17a² = 33 - 16a

To solve this equation, we'll rearrange it to the form of a quadratic equation and set it equal to zero:

17a² + 16a - 33 = 0

Now we can factor the quadratic equation or use the quadratic formula. Let's factor the equation:

(17a - 11)(a + 3) = 0

Setting each factor equal to zero, we get:

17a - 11 = 0 or a + 3 = 0

Solving these equations, we find:

17a = 11 or a = -3

a = 11/17 or a = -3

So the solutions to the equation are a = 11/17 and a = -3.