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Solve by completing the square:
{x}^(2) + 10x - 24 = 0

User Liona
by
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1 Answer

6 votes

Let's solve the given equation using completing the square:


\text{ x}^2\text{ + 10x - 24 = 0}

Step 1: Keep x terms on the left and move the constant to the right side by adding it on both sides.


\text{ x}^2\text{ + 10x - 24 = 0}
\text{ x}^2\text{ + 10x - 24 + 24 = 0 + 24}
\text{ x}^2\text{ + 10x = 24}

Step 2: Take half of the x term and square it.


\text{ x term = 10x}
((b)/(2))^2\text{ = (}(10)/(2))^2=5^2\text{ = 25}

Step 3: Add the result to both sides.


\text{ x}^2\text{ + 10x = 24}
\text{ (x}^2\text{ + 10x + 25) = 24 + 25}

Step 4: Rewrite the perfect square on the left and combine terms on the right.


\text{ (x}^2\text{ + 10x + 25) = 24 + 25}
(x+5)^2\text{ = 49}

Step 5: Square root of both sides.


√((x+5)^2)\text{ = }\sqrt{\text{49}}
\text{ x + 5 = }\pm\text{ 7}
\text{ x = }\pm\text{ 7 - 5}

Step 6: Solve for x.


x_1\text{ = 7 - 5 = 2}
x_2\text{ = -7 - 5 = -12}

Therefore, there are two solutions: x = 2 and -12.

User Marlen Schreiner
by
8.2k points

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