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3 years ago

How to solve 3p^2=-2p+4

Mathematics

1 answer:

harkovskaia [24]3 years ago

6 0

Answer:

Step-by-step explanation:

Simplifying

3p2 + -2p = 4

Reorder the terms:

-2p + 3p2 = 4

Solving

-2p + 3p2 = 4

Solving for variable 'p'.

Reorder the terms:

-4 + -2p + 3p2 = 4 + -4

Combine like terms: 4 + -4 = 0

-4 + -2p + 3p2 = 0

Begin completing the square. Divide all terms by

3 the coefficient of the squared term:

Divide each side by '3'.

-1.333333333 + -0.6666666667p + p2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.

-1.333333333 + -0.6666666667p + 1.333333333 + p2 = 0 + 1.333333333

Reorder the terms:

-1.333333333 + 1.333333333 + -0.6666666667p + p2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000

0.000000000 + -0.6666666667p + p2 = 0 + 1.333333333

-0.6666666667p + p2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333

-0.6666666667p + p2 = 1.333333333

The p term is -0.6666666667p. Take half its coefficient (-0.3333333334).

Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.

-0.6666666667p + 0.1111111112 + p2 = 1.333333333 + 0.1111111112

Reorder the terms:

0.1111111112 + -0.6666666667p + p2 = 1.333333333 + 0.1111111112

Combine like terms: 1.333333333 + 0.1111111112 = 1.4444444442

0.1111111112 + -0.6666666667p + p2 = 1.4444444442

Factor a perfect square on the left side:

(p + -0.3333333334)(p + -0.3333333334) = 1.4444444442

Calculate the square root of the right side: 1.201850425

Break this problem into two subproblems by setting

(p + -0.3333333334) equal to 1.201850425 and -1.201850425.

Subproblem 1

p + -0.3333333334 = 1.201850425

Simplifying

p + -0.3333333334 = 1.201850425

Reorder the terms:

-0.3333333334 + p = 1.201850425

Solving

-0.3333333334 + p = 1.201850425

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '0.3333333334' to each side of the equation.

-0.3333333334 + 0.3333333334 + p = 1.201850425 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000

0.0000000000 + p = 1.201850425 + 0.3333333334

p = 1.201850425 + 0.3333333334

Combine like terms: 1.201850425 + 0.3333333334 = 1.5351837584

p = 1.5351837584

Simplifying

p = 1.5351837584

Subproblem 2

p + -0.3333333334 = -1.201850425

Simplifying

p + -0.3333333334 = -1.201850425

Reorder the terms:

-0.3333333334 + p = -1.201850425

Solving

-0.3333333334 + p = -1.201850425

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '0.3333333334' to each side of the equation.

-0.3333333334 + 0.3333333334 + p = -1.201850425 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000

0.0000000000 + p = -1.201850425 + 0.3333333334

p = -1.201850425 + 0.3333333334

Combine like terms: -1.201850425 + 0.3333333334 = -0.8685170916

p = -0.8685170916

Simplifying

p = -0.8685170916

Solution

The solution to the problem is based on the solutions

from the subproblems.

p = {1.5351837584, -0.8685170916}

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