Question

-40(-7х+5)=-1600 (-20х-50)2=100

Answer 1

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Answer 2

Let's solve the equations step by step:

Equation 1: -40(-7x + 5) = -1600

First, let's simplify the expression within the parentheses: -7x + 5

Distributing the -40 to each term inside the parentheses: 280x - 200 = -1600

Next, let's isolate the variable x by moving the constant term to the other side of the equation: 280x = -1600 + 200 280x = -1400

Dividing both sides of the equation by 280: x = -1400/280 x = -5

So the solution to the first equation is x = -5.

Equation 2: (-20x - 50)2 = 100

First, let's simplify the expression within the parentheses: -20x - 50

Squaring the expression: (-20x - 50)2 = 100 (-20x - 50)(-20x - 50) = 100

Expanding the equation: 400x^2 + 2000x + 2000x + 2500 = 100 400x^2 + 4000x + 2500 - 100 = 0 400x^2 + 4000x + 2400 = 0

Now, let's simplify the equation further: 4x^2 + 40x + 24 = 0

Dividing the entire equation by 4 to simplify: x^2 + 10x + 6 = 0

This quadratic equation doesn't factor easily, so we can use the quadratic formula to find the solutions. The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 10, and c = 6.

x = (-10 ± √(10^2 - 4(1)(6))) / (2(1)) x = (-10 ± √(100 - 24)) / 2 x = (-10 ± √76) / 2 x = (-10 ± √(4 * 19)) / 2 x = (-10 ± 2√19) / 2 x = -5 ± √19

So the solutions to the second equation are x = -5 + √19 and x = -5 - √19.