SOLUTION: Solve by completing the square. (When I do this, I get a LOT of fractions. I feel like I'm missing something big in this problem.) 8x^2+10x=3

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve by completing the square. (When I do this, I get a LOT of fractions. I feel like I'm missing something big in this problem.) 8x^2+10x=3      Log On


   

Question 1127312: Solve by completing the square.
(When I do this, I get a LOT of fractions. I feel like I'm missing something big in this problem.)
8x^2+10x=3
Found 3 solutions by josgarithmetic, MathLover1, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
8x%5E2%2B10x=3
8x%5E2%2B10x-3=0
or just start from original equation,
8%28x%5E2%2B%2810%2F8%29x%29=3
8%28x%5E2%2B%285%2F4%29x%29=3
8%28x%5E2%2B%285%2F4%29x%2B%285%2F8%29%5E2%29=3%2B8%285%2F8%29%5E2
8%28x%5E2%2B5%2F8%29%5E2=3%2B8%2A25%2F%288%2A8%29
%28x%2B5%2F8%29%5E2=3%2F8%2B%288%2F8%2925%2F%288%2A8%29
%28x%2B5%2F8%29%5E2=3%2F8%2B25%2F64
%28x%2B5%2F8%29%5E2=24%2F64%2B25%2F64
%28x%2B5%2F8%29%5E2=49%2F64
x%2B5%2F8=0%2B-+7%2F8, tooksquarerootbothsides

x=-5%2F8%2B-+7%2F8

x=-12%2F8=highlight%28-3%2F2%29
OR
highlight%28x=1%2F4%29
.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

8x%5E2%2B10x=3
8%28x%5E2%2B%2810%2F8%29x%29=3
8%28x%5E2%2B%2810%2F8%29x%29=3
8%28x%5E2%2B%285%2F4%29x%29-3+=0
8%28x%5E2%2B%285%2F4%29x+%2Bb%5E2%29-8b%5E2-3=0

coefficients: a=1, 2ab=%285%2F4%29

find b
2%2A1%2Ab=%285%2F4%29->b=%285%2F4%29%2F2->b=%285%2F8%29

8%28x%5E2%2B%285%2F4%29x+%2B%285%2F8%29%5E2%29-8%285%2F8%29%5E2-3=0
8%28x%2B5%2F8%29%5E2-cross%288%29%2825%2Fcross%2864%298%29-3=0
8%28x%2B5%2F8%29%5E2-25%2F8-3=0
8%28x%2B5%2F8%29%5E2-25%2F8-24%2F8=0
8%28x+%2B+5%2F8%29%5E2+-+49%2F8+=+0


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


You are likely to get fractions when completing the square, except in "nice" problems....

8x%5E2%2B10x+=+3

Factor out the leading coefficient:

8%28x%5E2%2B%285%2F4%29x%29+=+3

Take half the coefficient of the x term (5/8), square it (25/64), and add 25/64 in the parentheses on the left, to complete the square. Note that you added 8*25/64 = 25/8 on the left side of the equation, so you need to add 25/8 on the right to keep the equation balanced.

(Note that the only time you will NOT get fractions in the process of completing the square is when half the coefficient of x is an integer.)

8%28x%5E2%2B%285%2F4%29x%2B25%2F64%29+=+3%2B25%2F8

Write the expression in parentheses as the square of a binomial, and simplify the expression on the right:

8%28x%2B%285%2F8%29%29%5E2+=+49%2F8

Divide by 8 to get the squared binomial by itself:

x%2B%285%2F8%29%5E2+=+49%2F64

Take the square root of both sides, getting both positive and negative roots on the right:

x%2B5%2F8+=+7%2F8 OR x%2B5%2F8+=+-7%2F8

Solve the two equations to find the two roots of the original equation:

x+=+2%2F8+=+1%2F4 OR x+=+-12%2F8+=+-3%2F2

The two roots of the equation are 1/4 and -3/2.