SOLUTION: Find x in: 4x^2-16x+15=0

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Question 1040824: Find x in:
4x^2-16x+15=0
Found 3 solutions by josgarithmetic, josmiceli, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
What method do you want to use?

%28-16%29%5E2-4%2A4%2A15=256-240=16=4%5E2

The quadratic member is seems factorable. Look for the combinations of binomials which work(?). Further, if you do not want to test several factorizations, you now have the discriminant and can easily plug what you need into the general solution formula.


x=%2816%2B-+4%29%2F%282%2A4%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There should be 2 solutions, or roots.
either:
2 imaginary roots
or
2 real roots
-------------------
+4x%5E2+-+16x+%2B+15+=+0+
I can use the quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+4+
+b+=+-16+
+c+=+15+
+x+=+%28-%28-16%29+%2B-+sqrt%28+%28-16%29%5E2+-+4%2A4%2A15+%29%29+%2F+%282%2A4%29+
+x+=+%28+16+%2B-+sqrt%28+256+-+240+%29%29+%2F+8+
+x+=+%28+16+%2B+sqrt%28+16+%29+%29+%2F+8+
+x+=+%28+16+%2B+4+%29+%2F+8+
+x+=+5%2F2+
and
+x+=+%28+16+-+sqrt%28+16+%29+%29+%2F+8+
+x+=+%28+16+-+4+%29+%2F+8+
+x+=+3%2F2+
---------------
check the solutions:
+%28+x+-+3%2F2+%29%2A%28+x+-+5%2F2+%29+=+0+
+x%5E2+-%283%2F2%29%2Ax+-+%285%2F2%29%2Ax+%2B+15%2F4+=+0+
+x%5E2+-+4x+%2B+15%2F4+=+0+
Multiply both sides by +4+
+4x%5E2+-+16x+%2B+15+=+0+
OK

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Find x in:
4x^2-16x+15=0
4x%5E2+-+16x+%2B+15+=+0

%282x+-+5%29%282x+-+3%29+=+0

Set each binomial equal to 0, and solve