Question

3(х-7)в квадрате -2(х+7)(х-2)=(х+11) (х-4)+101

Answer 1

3(x-7)^2 - 2(x+7)(x-2)=(x+11)(x-4)+101
3(x^2-14x+49) - 2(x^2-2x+7x-14)=x^2-4x+11x-44+101
3x^2-42x+147-2x^2+4x-14x+28-x^2+4x-11x+44-101=0
-59x=118
x=118 : (-59)
x=-2

Answer 2

To solve the equation 3(x-7)^2 - 2(x+7)(x-2) = (x+11) + (x-4) + 101, we can follow a step-by-step process to simplify and solve for the value of x.

Step 1: Expand and Simplify

First, expand and simplify the left-hand side of the equation, then combine like terms on the right-hand side.

Step 2: Expand and Combine Like Terms

Expand and simplify the left-hand side of the equation using the distributive property and then combine like terms on the right-hand side of the equation.

Step 3: Solve for x

After expanding and simplifying, solve for the value of x.

Let's start by expanding and simplifying the equation in Step 1.

Step 1: Expand and Simplify

The given equation is: 3(x-7)^2 - 2(x+7)(x-2) = (x+11) + (x-4) + 101

Expanding the left-hand side: 3(x^2 - 14x + 49) - 2(x^2 - 2x + 7x - 14) = x + 11 + x - 4 + 101

Expanding further: 3x^2 - 42x + 147 - 2x^2 + 4x - 14 = 2x + 108

Combining like terms: x^2 - 38x + 133 = 2x + 108

Now, the equation becomes: x^2 - 40x + 133 = 2x + 108

Step 2: Solve for x

To solve for x, we can rearrange the equation to set it equal to zero and then use the quadratic formula or factorization to find the solutions for x.

Rearranging the equation: x^2 - 42x + 133 - 2x - 108 = 0 x^2 - 42x - 2x + 133 - 108 = 0 x^2 - 44x + 25 = 0

Now, we can solve for x by using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 1, b = -44, and c = 25.

Plugging these values into the quadratic formula, we get: x = (-(-44) ± √((-44)^2 - 4*1*25)) / (2*1) x = (44 ± √(1936 - 100)) / 2 x = (44 ± √1836) / 2 x = (44 ± √1836) / 2 x ≈ (44 + √1836) / 2 x ≈ (44 - √1836) / 2

The solutions for x are: x ≈ 42.72 x ≈ 1.28

Therefore, the solutions for the given equation are x ≈ 42.72 and x ≈ 1.28.