Solve (25 x)^2 - 45^2 = x

Evaluate

(25 x)^{2} - 4 5^{2} = x

Subtract the terms

More Steps

625 x^{2} - 2025 = x

Move the expression to the left side

625 x^{2} - 2025 - x = 0

Rewrite in standard form

625 x^{2} - x - 2025 = 0

Substitute a= 625,b= - 1 and c= - 2025 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 625 ( - 2025 )}{2 \times 625}

Simplify the expression

x = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 625 ( - 2025 )}{1250}

Simplify the expression

More Steps

x = \frac{1 \pm 5062501}{1250}

Separate the equation into 2 possible cases

x = \frac{1 + 5062501}{1250} x = \frac{1 - 5062501}{1250}

Solution

x_{1} = \frac{1 - 5062501}{1250}, x_{2} = \frac{1 + 5062501}{1250}

Alternative Form

x_{1} \approx - 1.7992, x_{2} \approx 1.8008

Solve the quadratic equation