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I can't solve 2t^2 + 5t - 63 = 0 -can you show me how?
- Thread starter ljones
- Start date
Re: I can't solve this-can you show me how?
You MAY be able to factor the expression on the left side.
Here's how I like to factor expressions where the coefficient of the squared term is something other than 1.
Multiply the coefficient of the squared term by the constant term. 2*(-63) = -126
Now, look for two numbers which MULTIPLY to -126, and which ADD to the middle coefficient, +5. With a little "trial and error," you should find that (-9)*(14) = -126, and that -9 + 14 = +5.
So, the numbers we're looking for are -9 and 14. Use these to rewrite the middle term:
2t[sup:1qtl2o49]2[/sup:1qtl2o49] - 9t + 14t - 63 = 0
Factor the left side by grouping the first two terms together, and the last two terms together:
(2t[sup:1qtl2o49]2[/sup:1qtl2o49] - 9t) + (14t - 63) = 0
Remove a common factor of t from the first group, and a factor of 7 from the last group:
t(2t - 9) + 7(2t - 9) = 0
Now, on the left side, (2t - 9) is a common factor. Remove that common factor from both terms, and you have
(2t - 9)(t + 7) = 0
The left side is factored. Use the Zero-product property. Set each of the factors equal to 0, and solve.
Either (2t - 9) = 0, OR (t + 7) = 0
You can take it from here.
ljones said:2t[sup:1qtl2o49]2[/sup:1qtl2o49] +5t-63 =0
You MAY be able to factor the expression on the left side.
Here's how I like to factor expressions where the coefficient of the squared term is something other than 1.
Multiply the coefficient of the squared term by the constant term. 2*(-63) = -126
Now, look for two numbers which MULTIPLY to -126, and which ADD to the middle coefficient, +5. With a little "trial and error," you should find that (-9)*(14) = -126, and that -9 + 14 = +5.
So, the numbers we're looking for are -9 and 14. Use these to rewrite the middle term:
2t[sup:1qtl2o49]2[/sup:1qtl2o49] - 9t + 14t - 63 = 0
Factor the left side by grouping the first two terms together, and the last two terms together:
(2t[sup:1qtl2o49]2[/sup:1qtl2o49] - 9t) + (14t - 63) = 0
Remove a common factor of t from the first group, and a factor of 7 from the last group:
t(2t - 9) + 7(2t - 9) = 0
Now, on the left side, (2t - 9) is a common factor. Remove that common factor from both terms, and you have
(2t - 9)(t + 7) = 0
The left side is factored. Use the Zero-product property. Set each of the factors equal to 0, and solve.
Either (2t - 9) = 0, OR (t + 7) = 0
You can take it from here.