# sqrt(3m^2 + 24) = 2m + 2. What is the sum of all the solutions to the equation? I know how to find the sum algebraically, but why can’t I use the -b/a formula here? Is it because there’s a radical? Thank you!

Whenever you have to square both sides to solve, you have to check for extraneous solutions. That tells you m could be 2 or –10, but because part of the solution was squaring both sides, you need to run both possible solutions through the original equation.Try 2 first: That works, now how about –10? Nope. Remember (more…)

# Test 7 Section 4 Question 6

Hi Mike…SAT 7, Section 4, Q6: I now see the shortcut here (that both sides of the equation are perfect squares,) but if I did expand and FOIL the left side, wouldn’t I still get the correct “a” values even though it takes longer? I can’t get it to work !! Can you please show the alternate path math steps? Or is recognizing the perfect squares the ONLY way to solve this one ? Thanks!

# PWN the SAT Math Guide p. 120 #9

PWN the SAT Math Guide p. 122 (p. 120 in newer printing) #9

h = -4.9^2 + t + 1.5
The equation … After how many seconds will the coin land on the ground?

When the coin lands, y=0, so we just need to solve the quadratic. Using the quadratic formula, however, I get a messy repeating decimal, not .664, .665. Could you solve this for me using the quadratic formula?

Also, I tried to search the Q&A here to see if you had already answered this question. Could you make an index for PWN the SAT Math Gu

# College Board Test 4 Section 3 #9

College Board Test 4 Section 3 #9:
____
√x-a = x-4
If a=2 what is the solution set of the preceding equation?
A. {3, 6}
B. {2}
C. {3}
D. {6}

Is there another way to solve this quickly besides plugging in the answer choices?

# Test 6 Section 3 #13

Test 6 Section 3 #13

# What is the set of all solutions to the equation square root of (x+2) = -x?

What is the set of all solutions to the equation square root of (x+2) = -x?

A) (-1,2) B) (-1), C) (2), D) There are no solutions.

Answer is (-1), but why won’t (-1,2) work? Square root of (2+2) = √4 = +/- 2, right?

# Test 8 Section 3 #14

Test 8 Section 3 #14

# PSAT #2, Section 4, #29

PSAT #2, Section 4, #29

# PSAT #2, Section 3, #16

PSAT #2, Section 3, #16

# PSAT #1, Section 4, #25

PSAT #1, Section 4, #25

# PSAT #1, Section 3, #17

PSAT #1, Section 3, #17

# PSAT #1, Section 3, #6

PSAT #1, Section 3, #6

# How would you do practise test 3, section 3, question 16? I plugged in 1 and happened to get the answer. But is there an algebraic way to do it?Thanks!

How would you do practise test 3, section 3, question 16? I plugged in 1 and happened to get the answer. But is there an algebraic way to do it?

Thanks!

# Can you explain #15 in Section 3 of test 4? I understand how to do the problem but was wondering if there is a shortcut or trick to seeing the correct answer?

Can you explain #15 in Section 3 of test 4? I understand how to do the problem but was wondering if there is a shortcut or trick to seeing the correct answer?

# Would you please explain the solution to Problem #31 in the calculator-allowed section of Practice Test #6?

Would you please explain the solution to Problem #31 in the calculator-allowed section of Practice Test #6?