First, if you're going to solve, you need to have an expression set to 0, so for the first problem, subtract 1 from both sides, leaving. 8x^2 + 4 = 0 Factor out a 4: 4(2x^2 + 1) = 0 Divide by 4: 2x^2 + 1 = 0 Now, isolate x: 2x^2 = -1 x^2 = -1/2 √(x^2) = √(-1/2) x = √(-1/2) Since you have the square root of a negative number, we remember the rules for taking roots; specifically √(ab) = √(a) * √(b), and √(a/b)= (√a)/(√b). Since (-1/2) = (-1)*(1/2), we know that x = √(-1) * √(1/2) By definition, √(-1) = i (imaginary number). x = i* (√1/√2) and since √1 = 1, then x = i * (1/√2) Now, because the (√) function only gives us the positive solution, we must include the opposite solution; and since I can't remember the ASCII code for the "plus or minus" symbol, we'll write it longhand x = +i/√2, -i/√2 Now, for your second problem, we'll do the same thing. 9x^2 + 7 = 4 9x^2 = -3 3x^2 = -1 x^2 = -1/3 x = (√-1)/(√3) x = i/√3, -i/√3
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Verified answer
isolate the variable, make the coefficient 1
9x-2=8x+5
9x-8x=2+5
x=2+5
x=7
First, if you're going to solve, you need to have an expression set to 0, so for the first problem, subtract 1 from both sides, leaving. 8x^2 + 4 = 0 Factor out a 4: 4(2x^2 + 1) = 0 Divide by 4: 2x^2 + 1 = 0 Now, isolate x: 2x^2 = -1 x^2 = -1/2 √(x^2) = √(-1/2) x = √(-1/2) Since you have the square root of a negative number, we remember the rules for taking roots; specifically √(ab) = √(a) * √(b), and √(a/b)= (√a)/(√b). Since (-1/2) = (-1)*(1/2), we know that x = √(-1) * √(1/2) By definition, √(-1) = i (imaginary number). x = i* (√1/√2) and since √1 = 1, then x = i * (1/√2) Now, because the (√) function only gives us the positive solution, we must include the opposite solution; and since I can't remember the ASCII code for the "plus or minus" symbol, we'll write it longhand x = +i/√2, -i/√2 Now, for your second problem, we'll do the same thing. 9x^2 + 7 = 4 9x^2 = -3 3x^2 = -1 x^2 = -1/3 x = (√-1)/(√3) x = i/√3, -i/√3
9x - 2 = 8x + 5
+2 +2
9x = 8x + 7
-8x -8x
x=7
Move all the unknowns to one side of the equation and then move the other numbers to the other side of the equation...like this...
9x - 2 = 8x + 5
+2 +2 ---->
9x = 8x +5 +2
-8x=-8x -------->
9x-8x = 5 +2
Add (or subtract) the numbers on each end....
9x-8x = 5 +2 ------->
1x=7
Then divide the answer by 1 to solve for x and BAM! There's your answer. Just break down the equation into simpler parts and then solve it.
7
x=7
9x – 2 = 8x + 5=
5+2=7
9x-8x=x
x=7
x = 7
x = 7
9x – 2 = 8x + 5
9x - 8x = 5+2
x = 7
9x-2=61
8x+5=61
x = 7