2z=(ax+y)^2+b equation
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The solution
Detail solution
Given the linear equation:
2*z = (a*x+y)^2+b
Expand brackets in the right part
2*z = a*x+y^2+b
Divide both parts of the equation by 2
z = b + (y + a*x)^2 / (2)
We get the answer: z = b/2 + (y + a*x)^2/2
2
b (y + a*x)
z_1 = - + ----------
2 2
$$z_{1} = \frac{\left(a x + y\right)^{2}}{2} + \frac{b}{2}$$
Sum and product of roots
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2
b (y + a*x)
- + ----------
2 2
$$\left(\frac{\left(a x + y\right)^{2}}{2} + \frac{b}{2}\right)$$
2
b (y + a*x)
- + ----------
2 2
$$\frac{\left(a x + y\right)^{2}}{2} + \frac{b}{2}$$
2
b (y + a*x)
- + ----------
2 2
$$\left(\frac{\left(a x + y\right)^{2}}{2} + \frac{b}{2}\right)$$
2
b (y + a*x)
- + ----------
2 2
$$\frac{\left(a x + y\right)^{2}}{2} + \frac{b}{2}$$