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12 April, 00:35

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

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  1. 12 April, 02:06
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    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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