Question

Solve the equation x² + 2x=43 Give your answer to 1 decimal place.



Found from Collins Maths Ks3 Higher Level​

Answer 1

Answer: It would need ten correct answers and one incorrect answer, ... 1 a an odd number (multiply the position in the sequence by 2 then subtract 1).

Step-by-step explanation:

Answer 2

Answer:

$x=-1+2\sqrt{11}, \quad x=-1-2\sqrt{11}$

Step-by-step explanation:

Given equation:

$x^2+2x=43$

Solve by the method of Completing the Square.

Step 1:  

When completing the square for an equation in the form ax² + bx + c = 0, the first step is to move the constant to the right side of the equation.  

This has already been done in the given equation:

$x^2+2x=43$

Step 2:  

Add the square of half the coefficient of x to both sides.  This forms a perfect square trinomial on the left side:

$\implies x^2+2x+\left(\dfrac{2}{2}\right)^2=43+\left(\dfrac{2}{2}\right)^2$

Simplify:

$\implies x^2+2x+\left(1\right)^2=43+\left(1\right)^2$

$\implies x^2+2x+1=43+1$

$\implies x^2+2x+1=44$

Step 3:  

Factor the perfect square trinomial on the left side to complete the square:

$\implies (x+1)^2=44$

Step 4:

To solve, square root both sides:

$\implies \sqrt{(x+1)^2}=\sqrt{44}$

$\implies x+1=\pm\sqrt{4 \cdot 11}$

$\implies x+1=\pm\sqrt{4}\sqrt{11}$

$\implies x+1=\pm2\sqrt{11}$

Subtract 1 from both sides:

$\implies x+1-1=-1\pm2\sqrt{11}$

$\implies x=-1\pm2\sqrt{11}$

Solution:

Therefore, the solutions of the given equation are:

$x=-1+2\sqrt{11}, \quad x=-1-2\sqrt{11}$