Question

2(4x+3)^2 −46=−12 quadratic formula

Answer 1

use quadratic equation

Answer 2

how can you go wrong in two ways, when the solution is so easy?
2(4x+3)^2 - 46 = -12
2(4x+3)^2 = 34
(4x+3)^2 = 17
4x+3 = ±√17
4x = -3±√17
x = (-3±√17)/4

Answer 3

To solve this equation using the quadratic formula, we need to rearrange it into the form ax^2 + bx + c = 0.

First, expand the equation:
2(4x+3)^2 - 46 = -12
8(4x^2 + 6x + 3^2) - 46 = -12
8(4x^2 + 6x + 9) - 46 = -12
32x^2 + 48x + 72 - 46 = -12
32x^2 + 48x + 26 = -12

Now bring all terms to one side to set it equal to zero:
32x^2 + 48x + 26 + 12 = 0
32x^2 + 48x + 38 = 0

Now we have our equation in the form ax^2 + bx + c = 0 where a = 32, b = 48, and c = 38.

Now we can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (-48 ± √(48^2 - 4*32*38)) / 2*32
x = (-48 ± √(2304 - 4864)) / 64
x = (-48 ± √(-2560)) / 64

Since the discriminant (√(-2560)) is negative, the equation has no real solutions.

Answer 4

To solve the equation 2(4x+3)^2 - 46 = -12 using the quadratic formula, we first need to expand and simplify the left side of the equation:

2(4x+3)^2 - 46 = -12
Expand the square: 2(16x^2 + 24x + 9) - 46 = -12
Distribute the 2: 32x^2 + 48x + 18 - 46 = -12
Combine like terms: 32x^2 + 48x - 28 = -12
Rearrange the equation: 32x^2 + 48x - 28 + 12 = 0
32x^2 + 48x - 16 = 0

Now, we can use the quadratic formula to find the solutions for x:
x = (-b ± √(b^2 - 4ac)) / 2a
Where a = 32, b = 48, and c = -16.

Plugging in these values, we get:
x = (-48 ± √(48^2 - 4*32*(-16))) / 2*32
x = (-48 ± √(2304 + 2048)) / 64
x = (-48 ± √4352) / 64
x = (-48 ± 66) / 64

Now, we have two possible solutions:
x1 = (-48 + 66) / 64 = 18 / 64 = 9 / 32
x2 = (-48 - 66) / 64 = -114 / 64 = -57 / 32

Therefore, the solutions to the equation 2(4x+3)^2 - 46 = -12 are x = 9/32 and x = -57/32.

Answer 5

You are absolutely correct, and I apologize for my mistake in the previous response. Thank you for pointing it out.

The correct way to solve the equation 2(4x+3)^2 - 46 = -12 is as follows:

2(4x+3)^2 - 46 = -12
2(4x+3)^2 = 34
(4x+3)^2 = 17
Taking the square root of both sides:
4x+3 = ±√17
4x = -3 ± √17
Dividing by 4 on both sides:
x = (-3 ± √17) / 4

Therefore, the correct solutions to the equation are x = (-3 + √17) / 4 and x = (-3 - √17) / 4.

Thank you for providing the correct solution.