SOLUTION: Please help me solve these: 5 x squared + 9x - 1 = 0 4 x sq + 12x + 7 = 0

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Question 236463: Please help me solve these:
5 x squared + 9x - 1 = 0
4 x sq + 12x + 7 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

5x%5E2%2B9x-1=0 Start with the given equation.


Notice that the quadratic 5x%5E2%2B9x-1 is in the form of Ax%5E2%2BBx%2BC where A=5, B=9, and C=-1


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%289%29+%2B-+sqrt%28+%289%29%5E2-4%285%29%28-1%29+%29%29%2F%282%285%29%29 Plug in A=5, B=9, and C=-1


x+=+%28-9+%2B-+sqrt%28+81-4%285%29%28-1%29+%29%29%2F%282%285%29%29 Square 9 to get 81.


x+=+%28-9+%2B-+sqrt%28+81--20+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-1%29 to get -20


x+=+%28-9+%2B-+sqrt%28+81%2B20+%29%29%2F%282%285%29%29 Rewrite sqrt%2881--20%29 as sqrt%2881%2B20%29


x+=+%28-9+%2B-+sqrt%28+101+%29%29%2F%282%285%29%29 Add 81 to 20 to get 101


x+=+%28-9+%2B-+sqrt%28+101+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%28-9%2Bsqrt%28101%29%29%2F%2810%29 or x+=+%28-9-sqrt%28101%29%29%2F%2810%29 Break up the expression.


So the solutions are x+=+%28-9%2Bsqrt%28101%29%29%2F%2810%29 or x+=+%28-9-sqrt%28101%29%29%2F%2810%29


which approximate to x=0.105 or x=-1.905




# 2


4x%5E2%2B12x%2B7=0 Start with the given equation.


Notice that the quadratic 4x%5E2%2B12x%2B7 is in the form of Ax%5E2%2BBx%2BC where A=4, B=12, and C=7


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%284%29%287%29+%29%29%2F%282%284%29%29 Plug in A=4, B=12, and C=7


x+=+%28-12+%2B-+sqrt%28+144-4%284%29%287%29+%29%29%2F%282%284%29%29 Square 12 to get 144.


x+=+%28-12+%2B-+sqrt%28+144-112+%29%29%2F%282%284%29%29 Multiply 4%284%29%287%29 to get 112


x+=+%28-12+%2B-+sqrt%28+32+%29%29%2F%282%284%29%29 Subtract 112 from 144 to get 32


x+=+%28-12+%2B-+sqrt%28+32+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-12+%2B-+4%2Asqrt%282%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-12%2B4%2Asqrt%282%29%29%2F%288%29 or x+=+%28-12-4%2Asqrt%282%29%29%2F%288%29 Break up the expression.


x+=+%28-3%2Bsqrt%282%29%29%2F%282%29 or x+=+%28-3-sqrt%282%29%29%2F%282%29 Reduce.


So the solutions are x+=+%28-3%2Bsqrt%282%29%29%2F%282%29 or x+=+%28-3-sqrt%282%29%29%2F%282%29


which approximate to x=-0.793 or x=-2.207