Question

Реши квадратное уравнение 4(5x−20)2−17(5x−20)+4=0 Помогите пожалуйста, очень срочно!!!!!!

Answer 1

Solving the Quadratic Equation

To solve the quadratic equation 4(5x−20)²−17(5x−20)+4=0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax² + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our case, the equation is in the form 4(5x−20)²−17(5x−20)+4=0, so we can identify a = 4, b = -17(5x−20), and c = 4.

Let's substitute these values into the quadratic formula and solve for x.

Applying the Quadratic Formula

Step 1: Identify the values of a, b, and c from the equation: - a = 4 - b = -17(5x−20) - c = 4

Step 2: Substitute the values into the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Step 3: Simplify the equation: x = (-(-17(5x−20)) ± √((-17(5x−20))² - 4 * 4 * 4)) / (2 * 4)

Step 4: Simplify further: x = (17(5x−20) ± √(289(5x−20)² - 64)) / 8

Step 5: Expand and simplify the expression inside the square root: x = (17(5x−20) ± √(289(25x² - 200x + 400) - 64)) / 8

Step 6: Simplify further: x = (17(5x−20) ± √(7225x² - 57800x + 115600 - 64)) / 8

Step 7: Simplify the expression inside the square root: x = (17(5x−20) ± √(7225x² - 57800x + 115536)) / 8

Now, we have the quadratic equation in the form x = (17(5x−20) ± √(7225x² - 57800x + 115536)) / 8.

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