Solve the equation by completing the square root round to the nearest hundredth if necessary X^2+3x=24

Mathematics

2 answers:

goldfiish [28.3K]3 years ago

8 0

Remember the formula (b/2)^2. The 3 is b, so (3/2)^2, which is 2.25. x^2+3x+2.25=26.25

marysya [2.9K]3 years ago

7 0

X^2 + 3x = 24

completing the square
(x + 1.5)^2 - 2.25 = 24

(x + 1.5)^2 = 26.25

x + 1.5 = +/- sqrt26.25 = +- 5.123

x = -1.5 + 5.123 = 3.62 to nearest hundredth and

x = -1.5 - 5.123 = -6.62 to nearest hundredth

solution set is {-6.62, 3.62}

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Please show your work this question what made you come to the conclusion. Thank you

AveGali [126]

Answer:

B the range, the x- and y-intercept

Step-by-step explanation:

the domain stays the same : all values of x are possible out of the interval (-infinity, +infinity).

but the range changes, as for the original function y could only have positive values - even for negative x.

the new function has a first term (with b) that can get very small for negative x, and then a subtraction of 2 makes the result negative.

the y-intercept (x=0) of the original function is simply y=1, as b⁰=1.

the y-intercept of the new function is definitely different, because the first term 3×(b¹) is larger than 3, because b is larger than 1. and a subtraction of 2 leads to a result larger than 1, which is different to 1.

the original function has no x-intercept (y=0), as this would happen only for x = -infinity. and that is not a valid value.

the new function has an x-intercept, because the y-values (range) go from negative to positive numbers. any continuous function like this must therefore have an x-intercept (again, y = the function result = 0)

$3 {b}^{x + 1} = 2$