Solve (30-x) 2 =x^252 - ScanMath

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Type your math problem... (30-x) 2 =x^252

Question

Solve the quadratic equation

Solve using the quadratic formula

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Solve by completing the square

Solve using the PQ formula

x_{1} = - \frac{1 + 3121}{52}, x_{2} = \frac{- 1 + 3121}{52}

Alternative Form

x_{1} \approx - 1.093575, x_{2} \approx 1.055114

Evaluate

(30 - x) \times 2 = x^{2} \times 52

Multiply the terms

2 (30 - x) = x^{2} \times 52

Use the commutative property to reorder the terms

2 (30 - x) = 52 x^{2}

Swap the sides

52 x^{2} = 2 (30 - x)

Expand the expression

More Steps

52 x^{2} = 60 - 2 x

Move the expression to the left side

52 x^{2} - 60 + 2 x = 0

Rewrite in standard form

52 x^{2} + 2 x - 60 = 0

Substitute a= 52,b= 2 and c= - 60 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 2 \pm 2 ^{2} - 4 \times 52 ( - 60 )}{2 \times 52}

Simplify the expression

x = \frac{- 2 \pm 2 ^{2} - 4 \times 52 ( - 60 )}{104}

Simplify the expression

More Steps

x = \frac{- 2 \pm 12484}{104}

Simplify the radical expression

More Steps

x = \frac{- 2 \pm 2 3121}{104}

Separate the equation into 2 possible cases

x = \frac{- 2 + 2 3121}{104} x = \frac{- 2 - 2 3121}{104}

Simplify the expression

More Steps

x = \frac{- 1 + 3121}{52} x = \frac{- 2 - 2 3121}{104}

Simplify the expression

More Steps

x = \frac{- 1 + 3121}{52} x = - \frac{1 + 3121}{52}

Solution

x_{1} = - \frac{1 + 3121}{52}, x_{2} = \frac{- 1 + 3121}{52}

Alternative Form

x_{1} \approx - 1.093575, x_{2} \approx 1.055114

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