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Popular >

solvefor x,tx=2-sqrt(x2-9)

Solution

solve for

x, t x = 2 - x^{2} - 9

Solution

x = \frac{2 t + - 9 t ^{2} + 13}{t ^{2} - 1} {- \frac{2}{3} \leq t < \frac{13}{3}}, x = \frac{2 t - - 9 t ^{2} + 13}{t ^{2} - 1} {- \frac{13}{3} < t \leq \frac{2}{3}}

Solution steps

t x = 2 - x^{2} - 9

Remove square roots

x^{2} t^{2} - 4 x t + 4 = x^{2} - 9

Solve

x^{2} t^{2} - 4 x t + 4 = x^{2} - 9 : x = \frac{2 t + - 9 t ^{2} + 13}{t ^{2} - 1}, x = \frac{2 t - - 9 t ^{2} + 13}{t ^{2} - 1}

x = \frac{2 t + - 9 t ^{2} + 13}{t ^{2} - 1}, x = \frac{2 t - - 9 t ^{2} + 13}{t ^{2} - 1}

Verify Solutions:

x = \frac{2 t + - 9 t ^{2} + 13}{t ^{2} - 1} {- \frac{2}{3} \leq t < \frac{13}{3}}, x = \frac{2 t - - 9 t ^{2} + 13}{t ^{2} - 1} {- \frac{13}{3} < t \leq \frac{2}{3}}

The solutions are

x = \frac{2 t + - 9 t ^{2} + 13}{t ^{2} - 1} {- \frac{2}{3} \leq t < \frac{13}{3}}, x = \frac{2 t - - 9 t ^{2} + 13}{t ^{2} - 1} {- \frac{13}{3} < t \leq \frac{2}{3}}

Popular Examples

sqrt(2x+21)-17=-14

2 x + 21 - 17 = - 14

sqrt(2x+7)+sqrt(3x+10)=2

2 x + 7 + 3 x + 10 = 2

x - 1 = 6 + 2 x

sqrt(5x+61)+14=20

5 x + 61 + 14 = 20

solvefor y,sqrt(xy)=1+x^2y solve for

y, x y = 1 + x^{2} y

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