Solve x^2-2x(1+3k)+7(3+2k)=0

Question

Solve the equation

Solve for x

Solve for k

x = 1 + 3 k + - 20 - 8 k + 9 k^{2} x = 1 + 3 k - - 20 - 8 k + 9 k^{2}

Evaluate

x^{2} - 2 x (1 + 3 k) + 7 (3 + 2 k) = 0

Rewrite the expression

x^{2} + (- 2 - 6 k) x + 21 + 14 k = 0

Substitute a= 1,b= - 2 - 6 k and c= 21 + 14 k into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{2 + 6 k \pm ( - 2 - 6 k ) ^{2} - 4 ( 21 + 14 k )}{2}

Simplify the expression

More Steps

x = \frac{2 + 6 k \pm - 80 - 32 k + 36 k ^{2}}{2}

Simplify the radical expression

More Steps

x = \frac{2 + 6 k \pm 2 - 20 - 8 k + 9 k ^{2}}{2}

Separate the equation into 2 possible cases

x = \frac{2 + 6 k + 2 - 20 - 8 k + 9 k ^{2}}{2} x = \frac{2 + 6 k - 2 - 20 - 8 k + 9 k ^{2}}{2}

Simplify the expression

More Steps

x = 1 + 3 k + - 20 - 8 k + 9 k^{2} x = \frac{2 + 6 k - 2 - 20 - 8 k + 9 k ^{2}}{2}

Solution

More Steps

x = 1 + 3 k + - 20 - 8 k + 9 k^{2} x = 1 + 3 k - - 20 - 8 k + 9 k^{2}

Show Solution