Solve by completing the square;round to the nearest hundredth if necessary.
x^2-3x=4
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1.C
2.C
3.B
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5.B
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x ^ 2 - 3 x = 4
The x-term coefficient = − 3
The half of the x-term coefficient = − 3 / 2
After squaring you have ( − 3 / 2 ) ^ 2= 9 / 4
x ^ 2 - 3 x = 4
Add 9 / 4 to both sides
x ^ 2 - 3 x + 9 / 4 = 4 + 9 / 4
x ^ 2 - 3 x + 9 / 4 = 16 / 4 + 9 / 4
x ^ 2 - 3 x + 9 / 4 = 25 / 4
Write the perfect square on the left side:
( x - 3 / 2 ) ^ 2 = 25 / 4
Take the square root of both sides:
x - 3 / 2 = sqroot ( 25 / 4 )
x - 3 / 2 = ± 5 / 2 Add 3 / 2 to both sides
x - 3 / 2 + 3 / 2 = ± 5 / 2 + 3 / 2
x = ± 5 / 2 + 3 / 2
x1 = 5 / 2 + 3 / 2 = 8 / 2 = 4
x2 = - 5 / 2 + 3 / 2 = - 2 / 2 = - 1
The solutions are :
x = - 1 and x = 4
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Remark:
x ^ 2 - 3 x + 9 / 4 = ( x - 3 / 2 ) ^ 2 becouse:
( x - 3 / 2 ) ^ 2 =
x ^ 2 - 2 * x * 3 / 2 + ( 3 / 2 ) ^ 2 =
x ^ 2 - x * 3 + 9 / 4 =
x ^ 2 - 3 x + 9 / 4
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To solve the equation x^2 - 3x = 4 by completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation.
x^2 - 3x - 4 = 0
Step 2: Take half of the coefficient of x, square it, and add it to both sides of the equation to complete the square.
In this case, half of -3 is -1.5, and (-1.5)^2 = 2.25.
x^2 - 3x + 2.25 = 4 + 2.25
x^2 - 3x + 2.25 = 6.25
Step 3: Rewrite the left side of the equation as a perfect square trinomial.
(x - 1.5)^2 = 6.25
Step 4: Take the square root of both sides of the equation.
x - 1.5 = ±√6.25
Step 5: Solve for x by adding 1.5 to both sides of the equation.
x = 1.5 ± √6.25
Now, round the solutions to the nearest hundredth if necessary:
x ≈ 1.5 + √6.25 ≈ 4.5
x ≈ 1.5 - √6.25 ≈ -1.5
Therefore, the solutions to the equation x^2 - 3x = 4, rounded to the nearest hundredth, are approximately 4.5 and -1.5.
x^2 - 3 x = 4
x^2 -3 x +(3/2)^2 = 4 + 9/4
(x-1.5)^2 = (1/4)(16 + 9)
(x-1.5)^2 = (1/4)(25) = 25/4
x-3/2 = +/- 5/2
x = 3/2 +/- 5/2
x = 4 or x = -1