Solve ( x1^2 x1 -2025)*x^2= 2m-2

Question

Solve the equation

Solve for x

Solve for m

x = \frac{4050 + 2 202 5 ^{2} - 8 + 8 m}{2} x = - \frac{4050 + 2 202 5 ^{2} - 8 + 8 m}{2} x = \frac{4050 - 2 202 5 ^{2} - 8 + 8 m}{2} x = - \frac{4050 - 2 202 5 ^{2} - 8 + 8 m}{2}

Evaluate

(x \times 1^{2} \times x \times 1 - 2025) x^{2} = 2 m - 2

Simplify

More Steps

x^{2} (x^{2} - 2025) = 2 m - 2

Expand the expression

More Steps

x^{4} - 2025 x^{2} = 2 m - 2

Move the expression to the left side

x^{4} - 2025 x^{2} - (2 m - 2) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x^{4} - 2025 x^{2} - 2 m + 2 = 0

Solve the equation using substitution t = x^{2}

t^{2} - 2025 t - 2 m + 2 = 0

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

t = \frac{2025 \pm ( - 2025 ) ^{2} - 4 ( - 2 m + 2 )}{2}

Simplify the expression

More Steps

t = \frac{2025 \pm 202 5 ^{2} + 8 m - 8}{2}

Separate the equation into 2 possible cases

t = \frac{2025 + 202 5 ^{2} + 8 m - 8}{2} t = \frac{2025 - 202 5 ^{2} + 8 m - 8}{2}

Substitute back

x^{2} = \frac{2025 + 202 5 ^{2} + 8 m - 8}{2} x^{2} = \frac{2025 - 202 5 ^{2} + 8 m - 8}{2}

Solve the equation for x

More Steps

x = \frac{4050 + 2 202 5 ^{2} - 8 + 8 m}{2} x = - \frac{4050 + 2 202 5 ^{2} - 8 + 8 m}{2} x^{2} = \frac{2025 - 202 5 ^{2} + 8 m - 8}{2}

Solution

More Steps

x = \frac{4050 + 2 202 5 ^{2} - 8 + 8 m}{2} x = - \frac{4050 + 2 202 5 ^{2} - 8 + 8 m}{2} x = \frac{4050 - 2 202 5 ^{2} - 8 + 8 m}{2} x = - \frac{4050 - 2 202 5 ^{2} - 8 + 8 m}{2}

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