Solve (20-x)^2 = 48^2 (44-x)^2

Question

Solve the quadratic equation

x_{1} = \frac{2132}{49}, x_{2} = \frac{2092}{47}

Alternative Form

x_{1} \approx 43.510204, x_{2} \approx 44.510638

Evaluate

(20 - x)^{2} = 4 8^{2} (44 - x)^{2}

Multiply the terms

(20 - x)^{2} = (2112 - 48 x)^{2}

Expand the expression

More Steps

400 - 40 x + x^{2} = (2112 - 48 x)^{2}

Expand the expression

More Steps

400 - 40 x + x^{2} = 211 2^{2} - 202752 x + 2304 x^{2}

Move the expression to the left side

400 + 202712 x - 2303 x^{2} - 211 2^{2} = 0

Rewrite in standard form

- 2303 x^{2} + 202712 x + 400 - 211 2^{2} = 0

Multiply both sides

2303 x^{2} - 202712 x - 400 + 211 2^{2} = 0

Substitute a= 2303,b= - 202712 and c= - 400 + 211 2^{2} into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{202712 \pm ( - 202712 ) ^{2} - 4 \times 2303 ( - 400 + 211 2 ^{2} )}{2 \times 2303}

Simplify the expression

x = \frac{202712 \pm ( - 202712 ) ^{2} - 4 \times 2303 ( - 400 + 211 2 ^{2} )}{4606}

Simplify the expression

More Steps

x = \frac{202712 \pm 20271 2 ^{2} + 3684800 - 9212 \times 211 2 ^{2}}{4606}

Simplify the radical expression

x = \frac{202712 \pm 8 2533 9 ^{2} + 57575 - 2303 \times 52 8 ^{2}}{4606}

Separate the equation into 2 possible cases

x = \frac{202712 + 8 2533 9 ^{2} + 57575 - 2303 \times 52 8 ^{2}}{4606} x = \frac{202712 - 8 2533 9 ^{2} + 57575 - 2303 \times 52 8 ^{2}}{4606}

Simplify the expression

More Steps

x = \frac{2092}{47} x = \frac{202712 - 8 2533 9 ^{2} + 57575 - 2303 \times 52 8 ^{2}}{4606}

Simplify the expression

More Steps

x = \frac{2092}{47} x = \frac{2132}{49}

Solution

x_{1} = \frac{2132}{49}, x_{2} = \frac{2092}{47}

Alternative Form

x_{1} \approx 43.510204, x_{2} \approx 44.510638

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