Solve (x a)^2 - 7 = 10x b

Question

Solve the equation

Solve for x

Solve for a

Solve for b

x = \frac{5 b + 25 b ^{2} + 7 a ^{2}}{a ^{2}} x = \frac{5 b - 25 b ^{2} + 7 a ^{2}}{a ^{2}}

Evaluate

(x a)^{2} - 7 = 10 x b

To raise a product to a power,raise each factor to that power

x^{2} a^{2} - 7 = 10 x b

Rewrite the expression

a^{2} x^{2} - 7 = 10 b x

Move the expression to the left side

a^{2} x^{2} - 7 - 10 b x = 0

Rewrite in standard form

a^{2} x^{2} - 10 b x - 7 = 0

Substitute a= a^{2},b= - 10 b and c= - 7 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{10 b \pm ( - 10 b ) ^{2} - 4 a ^{2} ( - 7 )}{2 a ^{2}}

Simplify the expression

More Steps

x = \frac{10 b \pm 100 b ^{2} + 28 a ^{2}}{2 a ^{2}}

Simplify the radical expression

More Steps

x = \frac{10 b \pm 2 25 b ^{2} + 7 a ^{2}}{2 a ^{2}}

Separate the equation into 2 possible cases

x = \frac{10 b + 2 25 b ^{2} + 7 a ^{2}}{2 a ^{2}} x = \frac{10 b - 2 25 b ^{2} + 7 a ^{2}}{2 a ^{2}}

Simplify the expression

More Steps

x = \frac{5 b + 25 b ^{2} + 7 a ^{2}}{a ^{2}} x = \frac{10 b - 2 25 b ^{2} + 7 a ^{2}}{2 a ^{2}}

Solution

More Steps

x = \frac{5 b + 25 b ^{2} + 7 a ^{2}}{a ^{2}} x = \frac{5 b - 25 b ^{2} + 7 a ^{2}}{a ^{2}}

Show Solution