Solve the following equation by graphing the related function.
1. 4x^2 + 8x = 32
A: ?
Use the Zero Product Property to solve the following equation.
2. x(x + 3) = 32
A: ?
3. Solve 3x^2 + 5 = 21. Round to the nearest hundredth.
A: x = 5.33
x = 5.0 or 5?
1.
4x^2 + 8x = 32
4x^2 + 8x - 32 = 0
x^2 + 2x - 8 = 0
let y = x^2 + 2x - 8
now graph this, and look at where it crosses the x-axis.
From Wolfram's graph
http://www.wolframalpha.com/input/?i=y+%3D+x%5E2+%2B+2x+-+8
we can see x = -4 or x = 2
2.
x(x + 3) = 32
x^2 + 3x - 32 = 0
This does not factor over the rationals.
Since it asked to use the "zero product property" I was expecting it to factor. Is there a typo
(the fact that both #1 and #2 have 32 on the right side, might suggest a typo)
3.
3x^2 + 5 = 21
3x^2 = 16
x^2 = 16/3
x = ± 4/√3 = appr ± 2.31
Again, I suspect a typo, since your solution of x = 5.33 doesn't even come close as a solution
To solve the first equation, 4x^2 + 8x = 32, by graphing the related function, you would follow these steps:
1. Rewrite the equation in standard form: 4x^2 + 8x - 32 = 0.
2. Next, graph the related function y = 4x^2 + 8x - 32.
3. Determine the x-values where the graph intersects the x-axis. These are the solutions to the equation.
To solve the second equation, x(x + 3) = 32, using the Zero Product Property, follow these steps:
1. Set each factor equal to zero: x = 0 and x + 3 = 0.
2. Solve each equation separately:
For x = 0, x = 0.
For x + 3 = 0, subtract 3 from both sides to get x = -3.
3. The solutions to the equation are x = 0 and x = -3.
To solve the third equation, 3x^2 + 5 = 21, and round to the nearest hundredth, follow these steps:
1. Rewrite the equation in standard form: 3x^2 + 5 - 21 = 0, which simplifies to 3x^2 - 16 = 0.
2. Solve the quadratic equation using the quadratic formula or factoring.
3. By applying the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, where a = 3, b = 0, and c = -16:
x = (-0 ± √(0^2 - 4(3)(-16))) / (2(3))
x = (± √192) / 6
4. Simplify further:
x = (± √(64 * 3)) / 6
x = (± √64 * √3) / 6
x = (± 8 * √3) / 6
x = (± 4 * √3) / 3
5. Rounding to the nearest hundredth, x is approximately 5.33.
So, the solutions to the equation, rounded to the nearest hundredth, are x = 5.33 or x = 5.0