Question

-х в квадратe +7х-10=0 4х в квадратe +4х+1=0 1. х в квадратe -6х-16=0 2. х в квадратe +2х-15=0 3. 6х в квадратe -7+1=0 4. 7х в квадратe +9х+2=0 5. 3х в квадратe -12х=0 6. 4х в квадратe -х=0 7. 2х в квадратe -32=0 помогитe пожалуйста, нe успeваю рeшить

Answer 1

1) D=3^2
x1= 5
X2= 2
2)D=0
x=(-1/2)
3) D= 10
x1=(-2)
x2=8
4)D=8
x1=(-5)
x2=3
5)6x^2=6
x=+1;(-1)
6) D=5
x1=(-1)
x2= (-2/7)
7) x(3x-12)=0
x1=0
x2=4
8) x(4x-1)=0
x1=0
x2=1/4
9) 2x^2=32
x^2=16
x1=4
x2=(-4)

Answer 2

Quadratic Equations

To solve the given quadratic equations, we can use the quadratic formula or factorization method. Let's solve each equation step by step.

1. Equation: x^2 + 7x - 10 = 0 To solve this equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 1, b = 7, and c = -10. Substituting these values into the quadratic formula, we get:

x = (-7 ± √(7^2 - 4(1)(-10))) / (2(1))

Simplifying further:

x = (-7 ± √(49 + 40)) / 2

x = (-7 ± √89) / 2

Therefore, the solutions to the equation are:

x = (-7 + √89) / 2 and x = (-7 - √89) / 2 [[1]].

2. Equation: x^2 + 4x + 1 = 0 To solve this equation, we can again use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 1, b = 4, and c = 1. Substituting these values into the quadratic formula, we get:

x = (-4 ± √(4^2 - 4(1)(1))) / (2(1))

Simplifying further:

x = (-4 ± √(16 - 4)) / 2

x = (-4 ± √12) / 2

Therefore, the solutions to the equation are:

x = (-4 + √12) / 2 and x = (-4 - √12) / 2 [[2]].

3. Equation: 6x^2 - 7x + 1 = 0 To solve this equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 6, b = -7, and c = 1. Substituting these values into the quadratic formula, we get:

x = (-(-7) ± √((-7)^2 - 4(6)(1))) / (2(6))

Simplifying further:

x = (7 ± √(49 - 24)) / 12

x = (7 ± √25) / 12

Therefore, the solutions to the equation are:

x = (7 + √25) / 12 and x = (7 - √25) / 12 [[3]].

4. Equation: 7x^2 + 9x + 2 = 0 To solve this equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 7, b = 9, and c = 2. Substituting these values into the quadratic formula, we get:

x = (-9 ± √(9^2 - 4(7)(2))) / (2(7))

Simplifying further:

x = (-9 ± √(81 - 56)) / 14

x = (-9 ± √25) / 14

Therefore, the solutions to the equation are:

x = (-9 + √25) / 14 and x = (-9 - √25) / 14 [[4]].

5. Equation: 3x^2 - 12x = 0 To solve this equation, we can factor out the common term x:

x(3x - 12) = 0

Setting each factor equal to zero, we get:

x = 0 and 3x - 12 = 0

Solving the second equation for x:

3x = 12

x = 4

Therefore, the solutions to the equation are:

x = 0 and x = 4 [[5]].

6. Equation: 4x^2 - x = 0 To solve this equation, we can factor out the common term x:

x(4x - 1) = 0

Setting each factor equal to zero, we get:

x = 0 and 4x - 1 = 0

Solving the second equation for x:

4x = 1

x = 1/4

Therefore, the solutions to the equation are:

x = 0 and x = 1/4 [[6]].

7. Equation: 2x^2 - 32 = 0 To solve this equation, we can factor out the common term 2:

2(x^2 - 16) = 0

Setting each factor equal to zero, we get:

x^2 - 16 = 0

This equation can be further factored as the difference of squares:

(x - 4)(x + 4) = 0

Setting each factor equal to zero, we get:

x - 4 = 0 and x + 4 = 0

Solving for x, we get:

x = 4 and x = -4

Therefore, the solutions to the equation are:

x = 4 and x = -4 [[7]].

I hope this helps! Let me know if you have any further questions.