Exploring Simple Quadratic Equations

The video tutorial explains how to solve the equation 2x squared plus 3 equals 75. It begins by isolating the x squared term by subtracting 3 from both sides, resulting in 2x squared equals 72. Then, both sides are divided by 2 to get x squared equals 36. The solution for x is found by taking the square root of both sides, yielding x equals plus or minus 6. The tutorial concludes by verifying the solutions by substituting them back into the original equation, confirming that both positive and negative 6 satisfy the equation.

What is the first step to isolate x squared in the equation 2x^2 + 3 = 75?

• Divide both sides by 2

• Add 3 to both sides

• Multiply both sides by 2

• Subtract 3 from both sides

What is the result on the right-hand side after subtracting 3 from both sides?

• 69

• 36

• 78

• 72

What operation is performed to both sides to isolate x squared?

• Subtraction

• Multiplication

• Division

• Addition

What is the value of x squared after dividing both sides by 2?

• 144

• 18

• 72

• 36

What are the possible values of x after taking the square root of both sides?

• 0

• +/- 6

• -6

• +6

Why are there two solutions for x?

• Because x can only be positive

• Because x squared equals 36

• Because the equation is linear

• Because x cannot be zero

What verifies that x = +6 is a solution to the original equation?

• 6^2 + 3 = 75

• 2(6)^2 - 3 = 72

• 2(-6)^2 + 3 = 72

• 2(6)^2 + 3 = 75

Does x = -6 also satisfy the original equation?

• No, because negative numbers are not allowed

• No, because it results in a different value

• Yes, because (-6)^2 = 36

• Yes, but only in certain conditions

What is the result of 2(-6)^2 + 3?

• 75

• 72

• 36

• 69

Why is it important to check both positive and negative solutions in quadratic equations?

• Because only positive solutions are correct

• To ensure all possible solutions are considered

• Because negative solutions are not valid

• To make the equation more complex