Question

-2(2x-3)(2x+3)+7(x+3)^2=-(1-x)^2

Answer 1

-2(4x^2+6x-6x-9)+7(x^2+6x+9)=-1+2x-x^2
-8x^2+18+7x^2+42x+63=-1+2x-x^2
-8x^2+18+7x^2+42x+63+1-2x+x^2=0
40x+82=0
40x=-82
x=-82/40
x=-2.05

Answer 2

To solve the equation -2(2x-3)(2x+3) + 7(x+3)^2 = -(1-x)^2, you can follow these steps:

Step 1: Expand and simplify both sides of the equation. -2(2x-3)(2x+3) + 7(x+3)^2 = -(1-x)^2

Start by expanding each side:

-2(4x^2 - 9) + 7(x^2 + 6x + 9) = (1-x)^2

Now, simplify further:

-8x^2 + 18 + 7x^2 + 42x + 63 = (1-x)^2

Step 2: Expand the square on the right side of the equation.

(1-x)^2 = 1 - 2x + x^2

So, the equation becomes:

-8x^2 + 18 + 7x^2 + 42x + 63 = 1 - 2x + x^2

Step 3: Rearrange and combine like terms on both sides of the equation.

Combine like terms on both sides:

-8x^2 + 7x^2 - x^2 + 42x + 2x - 18 - 63 - 1 = 0

Now, simplify further:

-2x^2 + 44x - 82 = 0

Step 4: Divide the entire equation by -2 to make the coefficients more manageable:

x^2 - 22x + 41 = 0

Step 5: Solve the quadratic equation for x. You can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = -22, and c = 41. Plug these values into the formula:

x = (-(-22) ± √((-22)² - 4(1)(41))) / (2(1))

Simplify:

x = (22 ± √(484 - 164)) / 2 x = (22 ± √320) / 2

Now, simplify the square root:

x = (22 ± √(16 * 20)) / 2 x = (22 ± 4√5) / 2

Finally, divide both the numerator and denominator by 2:

x = 11 ± 2√5

So, the solutions for the equation -2(2x-3)(2x+3) + 7(x+3)^2 = -(1-x)^2 are:

x = 11 + 2√5 x = 11 - 2√5