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-4x²-7x =-36
What is the positive solution to the given equation?

\( 4x^2+19=32x+r \) 
In the given equation, r is a constant. The equation has exactly one real solution. What is the value of r?

\( x\left(kx-112\right)=-16 \) 
In the given equation, k is an integer constant. If the equation has two distinct real solutions, what is the greatest possible value of k?

\( r^2+qr=8r-97 \) 
In the given equation, q is an integer constant. The given equation has no real solution. What is the largest possible value of q?

y = -1.5
y = x² + 8x + a
In the given system of equations, a is a positive constant. The system has exactly one distinct real solution. What is the value of a?

\( kx^2-16x=24x^2-8 \) 
In the given equation, k is an integer constant. If the equation has two distinct real solutions, what is the greatest possible value of k?

\( r^2+qr=2r-55 \) 
In the given equation, q is an integer constant. The given equation has no real solutions. What is the largest possible value of q?

y = 2x² − 21x + 64
y = 3x + a
In the given system of equations, a is a constant. The graphs of the equations in the given system intersect  at exactly one point, (x, y), in the xy-plane. What is the value of a ?

\( y=-1.5 \) 
\( y=x^2+4x+a \) 
In the given system of equations, a is a positive integer constant. The system has no real solutions. What is the least possible value of a?

y =-6.5
y = x²+ 8x＋a
ln the given system of equations, a is a positive integer constant.The system has no real solutions. what is the least possible value of a?

−x² + bx − 676 = 0
In the given equation, b is a positive integer. The  equation has no real solution. What is the greatest possible value of b ?

\( y=x^2-37x \) 
\( y=-\frac{1}{4}(108x+k) \) 
The graphs of the equations in the given system intersect at exactly one point \( (x,\ y) \) in the xy-plane. What is the value of x ?