Solve 2(x-3)^2 19=37

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{114 - 1406}{38}, x_{2} = \frac{114 + 1406}{38}

Alternative Form

x_{1} \approx 2.013246, x_{2} \approx 3.986754

Evaluate

2 (x - 3)^{2} \times 19 = 37

Multiply the terms

38 (x - 3)^{2} = 37

Expand the expression

More Steps

38 x^{2} - 228 x + 342 = 37

Move the expression to the left side

38 x^{2} - 228 x + 305 = 0

Substitute a= 38,b= - 228 and c= 305 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{228 \pm ( - 228 ) ^{2} - 4 \times 38 \times 305}{2 \times 38}

Simplify the expression

x = \frac{228 \pm ( - 228 ) ^{2} - 4 \times 38 \times 305}{76}

Simplify the expression

More Steps

x = \frac{228 \pm 5624}{76}

Simplify the radical expression

More Steps

x = \frac{228 \pm 2 1406}{76}

Separate the equation into 2 possible cases

x = \frac{228 + 2 1406}{76} x = \frac{228 - 2 1406}{76}

Simplify the expression

More Steps

x = \frac{114 + 1406}{38} x = \frac{228 - 2 1406}{76}

Simplify the expression

More Steps

x = \frac{114 + 1406}{38} x = \frac{114 - 1406}{38}

Solution

x_{1} = \frac{114 - 1406}{38}, x_{2} = \frac{114 + 1406}{38}

Alternative Form

x_{1} \approx 2.013246, x_{2} \approx 3.986754

Show Solution