Solve the given Quadratic equation and give your answer in two significant figures 2x^2 +x -4 =O
Answers
Answer:
(x - 9)(x - 9) = 12
Simplifying
(x + -9)(x + -9) = 12
Reorder the terms:
(-9 + x)(x + -9) = 12
Reorder the terms:
(-9 + x)(-9 + x) = 12
Multiply (-9 + x) * (-9 + x)
(-9(-9 + x) + x(-9 + x)) = 12
((-9 * -9 + x * -9) + x(-9 + x)) = 12
((81 + -9x) + x(-9 + x)) = 12
(81 + -9x + (-9 * x + x * x)) = 12
(81 + -9x + (-9x + x2)) = 12
Combine like terms: -9x + -9x = -18x
(81 + -18x + x2) = 12
Solving
81 + -18x + x2 = 12
Solving for variable 'x'.
Reorder the terms:
81 + -12 + -18x + x2 = 12 + -12
Combine like terms: 81 + -12 = 69
69 + -18x + x2 = 12 + -12
Combine like terms: 12 + -12 = 0
69 + -18x + x2 = 0
Begin completing the square.
Move the constant term to the right:
Add '-69' to each side of the equation.
69 + -18x + -69 + x2 = 0 + -69
Reorder the terms:
69 + -69 + -18x + x2 = 0 + -69
Combine like terms: 69 + -69 = 0
0 + -18x + x2 = 0 + -69
-18x + x2 = 0 + -69
Combine like terms: 0 + -69 = -69
-18x + x2 = -69
The x term is -18x. Take half its coefficient (-9).
Square it (81) and add it to both sides.
Add '81' to each side of the equation.
-18x + 81 + x2 = -69 + 81
Reorder the terms:
81 + -18x + x2 = -69 + 81
Combine like terms: -69 + 81 = 12
81 + -18x + x2 = 12
Factor a perfect square on the left side:
(x + -9)(x + -9) = 12
Calculate the square root of the right side: 3.464101615
Break this problem into two subproblems by setting
(x + -9) equal to 3.464101615 and -3.464101615.
Subproblem 1
x + -9 = 3.464101615
Simplifying
x + -9 = 3.464101615
Reorder the terms:
-9 + x = 3.464101615
Solving
-9 + x = 3.464101615
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + x = 3.464101615 + 9
Combine like terms: -9 + 9 = 0
0 + x = 3.464101615 + 9
x = 3.464101615 + 9
Combine like terms: 3.464101615 + 9 = 12.464101615
x = 12.464101615
Simplifying
x = 12.464101615
Subproblem 2
x + -9 = -3.464101615
Simplifying
x + -9 = -3.464101615
Reorder the terms:
-9 + x = -3.464101615
Solving
-9 + x = -3.464101615
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + x = -3.464101615 + 9
Combine like terms: -9 + 9 = 0
0 + x = -3.464101615 + 9
x = -3.464101615 + 9
Combine like terms: -3.464101615 + 9 = 5.535898385
x = 5.535898385
Simplifying
x = 5.535898385
Solution
The solution to the problem is based on the solutions
from the subproblems.