Mathematics, 27.09.2019 23:00 kayranicole1

Solve the equation using inverse operations. check your solutions. in your final answer, include all of your work.
5 - 2x^2 = -15

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Answer from: maddieb1011

5-2x2=-15

Two solutions were found :

x = ± √10 = ± 3.1623

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

5-2*x^2-(-15)=0

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(5 - 2x2) - -15 = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

20 - 2x2 = -2 • (x2 - 10)

Trying to factor as a Difference of Squares :

3.2 Factoring: x2 - 10

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 10 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step 3 :

-2 • (x2 - 10) = 0

Step 4 :

Equations which are never true :

4.1 Solve : -2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.2 Solve : x2-10 = 0

Add 10 to both sides of the equation :

x2 = 10

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 10

The equation has two real solutions

These solutions are x = ± √10 = ± 3.1623

Two solutions were found :

x = ± √10 = ± 3.1623

Answer from: Quest

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.

Answer from: Quest

answer:

given the linear inequality : $x-2y\geq -12$

add 2y to both sides we get;

$x-2y+2y\geq -12+2y$

simplify:

$x\geq -12+2y$

add 12 to both sides of an equation;

$x+12\geq -12+2y+12$

simplify:

$x+12\geq 2y$

divide both sides by 2 we get;

$\frac{x}{2} + 6 \geq y$

$y\leq \frac{x}{2} + 6$

the related equation for the inequality equation [1] is;

$y =\frac{x}{2} +6$

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

$y =\frac{0}{2} +6$

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

$0 =\frac{x}{2} +6$

subtract 6 from both sides we get

$0-6 =\frac{x}{2} +6-6$

$-6 =\frac{x}{2}$

multiply both sides by 2 we get;

$-6 \times 2=x$

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.

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