What is 5x^2-7x-3=8 by solving using a graph?

Question

Mathematics

Leon Davila

5 January, 11:52

What is 5x^2-7x-3=8 by solving using a graph?

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Answers (1)

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Squeeky · Answer 1

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}