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Mathematics
Sadie
12 April, 00:35
What is 5x^2-7x-3=8 by solving using a graph?
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Caitlyn Calhoun
12 April, 02:06
0
Hello!
Simplifying
5x2 + - 7x + - 3 = 8
Reorder the terms:
-3 + - 7x + 5x2 = 8
Solving
-3 + - 7x + 5x2 = 8
Solving for variable 'x'.
Reorder the terms:
-3 + - 8 + - 7x + 5x2 = 8 + - 8
Combine like terms: - 3 + - 8 = - 11
-11 + - 7x + 5x2 = 8 + - 8
Combine like terms: 8 + - 8 = 0
-11 + - 7x + 5x2 = 0
Begin completing the square. Divide all terms by
5 the coefficient of the squared term:
Divide each side by '5'.
-2.2 + - 1.4x + x2 = 0
Move the constant term to the right:
Add '2.2' to each side of the equation.
-2.2 + - 1.4x + 2.2 + x2 = 0 + 2.2
Reorder the terms:
-2.2 + 2.2 + - 1.4x + x2 = 0 + 2.2
Combine like terms: - 2.2 + 2.2 = 0.0
0.0 + - 1.4x + x2 = 0 + 2.2
-1.4x + x2 = 0 + 2.2
Combine like terms: 0 + 2.2 = 2.2
-1.4x + x2 = 2.2
The x term is - 1.4x. Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.
Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 2.2 + 0.49
Reorder the terms:
0.49 + - 1.4x + x2 = 2.2 + 0.49
Combine like terms: 2.2 + 0.49 = 2.69
0.49 + - 1.4x + x2 = 2.69
Factor a perfect square on the left side:
(x + - 0.7) (x + - 0.7) = 2.69
Calculate the square root of the right side: 1.640121947
Break this problem into two subproblems by setting
(x + - 0.7) equal to 1.640121947 and - 1.640121947.
Subproblem 1
x + - 0.7 = 1.640121947
Simplifying
x + - 0.7 = 1.640121947
Reorder the terms:
-0.7 + x = 1.640121947
Solving
-0.7 + x = 1.640121947
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 1.640121947 + 0.7
Combine like terms: - 0.7 + 0.7 = 0.0
0.0 + x = 1.640121947 + 0.7
x = 1.640121947 + 0.7
Combine like terms: 1.640121947 + 0.7 = 2.340121947
x = 2.340121947
Simplifying
x = 2.340121947
Subproblem 2
x + - 0.7 = - 1.640121947
Simplifying
x + - 0.7 = - 1.640121947
Reorder the terms:
-0.7 + x = - 1.640121947
Solving
-0.7 + x = - 1.640121947
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = - 1.640121947 + 0.7
Combine like terms: - 0.7 + 0.7 = 0.0
0.0 + x = - 1.640121947 + 0.7
x = - 1.640121947 + 0.7
Combine like terms: - 1.640121947 + 0.7 = - 0.940121947
x = - 0.940121947
Simplifying
x = - 0.940121947
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.340121947, - 0.940121947}
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