What is the answer to sqrt(4x^2-4x+1)+(x+4)=a+7 ?

The answer to sqrt(4x^2-4x+1)+(x+4)=a+7 is x=(a+4)/3 {a>=-5/2 },x=-a-2 {a>=-5/2 }

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sqrt(4x^2-4x+1)+(x+4)=a+7

4 x^{2} - 4 x + 1 + (x + 4) = a + 7

x = \frac{a + 4}{3} {a \geq - \frac{5}{2}}, x = - a - 2 {a \geq - \frac{5}{2}}

Solution steps

4 x^{2} - 4 x + 1 + (x + 4) = a + 7

Remove square roots

4 x^{2} - 4 x + 1 = - 2 a x + x^{2} - 6 x + a^{2} + 6 a + 9

Solve

4 x^{2} - 4 x + 1 = - 2 a x + x^{2} - 6 x + a^{2} + 6 a + 9 : x = \frac{a + 4}{3}, x = - a - 2

x = \frac{a + 4}{3}, x = - a - 2

Verify Solutions:

x = \frac{a + 4}{3} {a \geq - \frac{5}{2}}, x = - a - 2 {a \geq - \frac{5}{2}}

The solutions are

x = \frac{a + 4}{3} {a \geq - \frac{5}{2}}, x = - a - 2 {a \geq - \frac{5}{2}}

7 x + 8 = x + 2

x - 5 + 1 = x

7 x - 5 = 3 x

10 x^{2} + 16 x = 5 x + 8

x^{2} + 5 + x - 3 = 0

What is the answer to sqrt(4x^2-4x+1)+(x+4)=a+7 ?
The answer to sqrt(4x^2-4x+1)+(x+4)=a+7 is x=(a+4)/3 {a>=-5/2 },x=-a-2 {a>=-5/2 }