Question

Find all real solutions to the equation 100x² + 20x + 1 = 16?

Answer 1

To find the real solutions to the equation 100x² + 20x + 1 = 16, rearrange the equation to 100x² + 20x - 15 = 0. Then, use the quadratic formula to find the solutions.

Step-by-step explanation:

To find all real solutions to the equation 100x² + 20x + 1 = 16, we can rearrange the equation to 100x² + 20x - 15 = 0.

Now, we need to solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values a = 100, b = 20, and c = -15 into the formula, we have:

x = (-20 ± √(20² - 4*100*(-15))) / (2*100)

After simplifying, the solutions are x ≈ -0.15 and x ≈ 0.1.

Answer 2

The real solutions to the equation 100x² + 20x + 1 = 16 are approximately 0.0253 and -0.0753.

Step-by-step explanation:

To find all real solutions to the equation 100x² + 20x + 1 = 16, we can rearrange the equation to the standard form of a quadratic equation: 100x² + 20x - 15 = 0. We can solve this equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values a = 100, b = 20, and c = -15 into the quadratic formula, we get:

x = (-20 ± √(20² - 4 * 100 * -15)) / (2 * 100)

Simplifying further, we have:

x = (-20 ± √(400 + 600))/200

x = (-20 ± √1000)/200

x = (-20 ± 10√10)/200

The two solutions to the equation are:

x₁ = (-20 + 10√10)/200 ≈ 0.0253

x₂ = (-20 - 10√10)/200 ≈ -0.0753