Let's start by expanding the left side of the equation:
(5x-3)(x+2) - (x+4)²
= 5x(x) + 5x(2) - 3(x) - 3(2) - (x+4)(x+4)
= 5x² + 10x - 3x - 6 - (x² + 4x + 4x + 16)
= 5x² + 10x - 3x - 6 - x² - 8x - 16
= 4x² - x - 22
Now, we solve for x by setting the equation equal to zero:
4x² - x - 22 = 0
This is a quadratic equation, so we can use the quadratic formula to find the solutions for x:
x = (-(-1) ± sqrt((-1)² - 4(4)(-22))) / 2(4)x = (1 ± sqrt(1 + 352)) / 8x = (1 ± sqrt(353)) / 8
Therefore, the solutions for x are:
x = (1 + sqrt(353)) / 8 and x = (1 - sqrt(353)) / 8
Let's start by expanding the left side of the equation:
(5x-3)(x+2) - (x+4)²
= 5x(x) + 5x(2) - 3(x) - 3(2) - (x+4)(x+4)
= 5x² + 10x - 3x - 6 - (x² + 4x + 4x + 16)
= 5x² + 10x - 3x - 6 - x² - 8x - 16
= 4x² - x - 22
Now, we solve for x by setting the equation equal to zero:
4x² - x - 22 = 0
This is a quadratic equation, so we can use the quadratic formula to find the solutions for x:
x = (-(-1) ± sqrt((-1)² - 4(4)(-22))) / 2(4)
x = (1 ± sqrt(1 + 352)) / 8
x = (1 ± sqrt(353)) / 8
Therefore, the solutions for x are:
x = (1 + sqrt(353)) / 8 and x = (1 - sqrt(353)) / 8