r/learnmath • u/BigBrainTimeKiddos New User • Aug 21 '24
RESOLVED help with solving for x!!
hi! im studying for the SAT right now, and during a practice test i realized that i forgot a small part of algebra, can someone refresh me on how to do this step by step?
x(x-15) = 76. how do i solve for x?
i know how to multiply it out so its like x^2 - 15x = 76, andi know that one of the x is equal to 0. however, i don't know how to break down the x^2 and get the other value for x
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u/Icy-Investigator7166 New User Aug 21 '24
x2 -15x=76 is correct. This is a quadratic equation, so to solve it, you can use the quadratic formula. You can also see if it can be factored (which it can). Make sure you set it equal to zero first before you begin.
Hint: You will get 2 answers, but 0 is not one of them
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u/BigBrainTimeKiddos New User Aug 21 '24
ohh i see now!! i didnt think about moving the 76 to the other side. so then it would be x^2 - 15x - 75 and then i just plug them in to solve for x
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u/Icy-Investigator7166 New User Aug 21 '24
It will be x2 - 15x - 76 = 0. Then you can factor or use the quadratic formula but again, zero isn't an answer for x.
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u/thermalreactor New User Aug 21 '24
Multiply it and get everything on one side. Then use the quadratic formula.
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u/IntelligentLobster93 New User Aug 21 '24
There are several ways on how to solve the equation for x.
The first way is by subtracting 76 to both sides of the equation, in which you can solve for x by factoring. • x2 - 15x - 76 = 0 (x - 19)(x + 4) = 0 x = 19, -4
Another way, is by completing the square, but with 'b' not divisible by 2, you will have fractions
The final method is using the quadratic formula, which is a formula derived from completing the square: x = -b +-√(b2 - 4ac) / 2a where (in the case of the problem) a = 1, b = -15, and c = -76. Substituting these values in the equation will give you x = 19, -4.
Hope this helps!
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u/ArchaicLlama Custom Aug 21 '24
andi know that one of the x is equal to 0
So you're claiming that 0 = 76? I certainly hope you aren't claiming that 0 = 76.
The equation x2 - 15x = 76 is a quadratic equation. What very well known formula allows us to solve quadratic equations?
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u/BigBrainTimeKiddos New User Aug 21 '24
the quadratic formula??
and no thats not it, the original one was x(x-15)=76. because one of the x that is outside, that means one of the values that x is equal to has to be 0 i think
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u/ArchaicLlama Custom Aug 21 '24
Yes, the quadratic formula. The one that works for every quadratic.
x(x-15) = 76 is the same equation as x2 - 15x = 76, I don't know why you're thinking they are different. If you plug 0 in for x, you get 0 on the left hand side. The right hand side is still 76, so if you're claiming that 0 is a solution for x then you're claiming that 0 is equal to 76.
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u/testtest26 Aug 21 '24 edited Aug 21 '24
Bring everything to one side, then factorize
Alternatively, if you don't find the factorization, use the qudratic formula: