240(x^2-4)=49x+500

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Solution for 240(x^2-4)=49x+500 equation:


Simplifying
240(x2 + -4) = 49x + 500

Reorder the terms:
240(-4 + x2) = 49x + 500
(-4 * 240 + x2 * 240) = 49x + 500
(-960 + 240x2) = 49x + 500

Reorder the terms:
-960 + 240x2 = 500 + 49x

Solving
-960 + 240x2 = 500 + 49x

Solving for variable 'x'.

Reorder the terms:
-960 + -500 + -49x + 240x2 = 500 + 49x + -500 + -49x

Combine like terms: -960 + -500 = -1460
-1460 + -49x + 240x2 = 500 + 49x + -500 + -49x

Reorder the terms:
-1460 + -49x + 240x2 = 500 + -500 + 49x + -49x

Combine like terms: 500 + -500 = 0
-1460 + -49x + 240x2 = 0 + 49x + -49x
-1460 + -49x + 240x2 = 49x + -49x

Combine like terms: 49x + -49x = 0
-1460 + -49x + 240x2 = 0

Begin completing the square.  Divide all terms by
240 the coefficient of the squared term: 

Divide each side by '240'.
-6.083333333 + -0.2041666667x + x2 = 0

Move the constant term to the right:

Add '6.083333333' to each side of the equation.
-6.083333333 + -0.2041666667x + 6.083333333 + x2 = 0 + 6.083333333

Reorder the terms:
-6.083333333 + 6.083333333 + -0.2041666667x + x2 = 0 + 6.083333333

Combine like terms: -6.083333333 + 6.083333333 = 0.000000000
0.000000000 + -0.2041666667x + x2 = 0 + 6.083333333
-0.2041666667x + x2 = 0 + 6.083333333

Combine like terms: 0 + 6.083333333 = 6.083333333
-0.2041666667x + x2 = 6.083333333

The x term is -0.2041666667x.  Take half its coefficient (-0.1020833334).
Square it (0.01042100696) and add it to both sides.

Add '0.01042100696' to each side of the equation.
-0.2041666667x + 0.01042100696 + x2 = 6.083333333 + 0.01042100696

Reorder the terms:
0.01042100696 + -0.2041666667x + x2 = 6.083333333 + 0.01042100696

Combine like terms: 6.083333333 + 0.01042100696 = 6.09375433996
0.01042100696 + -0.2041666667x + x2 = 6.09375433996

Factor a perfect square on the left side:
(x + -0.1020833334)(x + -0.1020833334) = 6.09375433996

Calculate the square root of the right side: 2.468553086

Break this problem into two subproblems by setting 
(x + -0.1020833334) equal to 2.468553086 and -2.468553086.

Subproblem 1

x + -0.1020833334 = 2.468553086 Simplifying x + -0.1020833334 = 2.468553086 Reorder the terms: -0.1020833334 + x = 2.468553086 Solving -0.1020833334 + x = 2.468553086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1020833334' to each side of the equation. -0.1020833334 + 0.1020833334 + x = 2.468553086 + 0.1020833334 Combine like terms: -0.1020833334 + 0.1020833334 = 0.0000000000 0.0000000000 + x = 2.468553086 + 0.1020833334 x = 2.468553086 + 0.1020833334 Combine like terms: 2.468553086 + 0.1020833334 = 2.5706364194 x = 2.5706364194 Simplifying x = 2.5706364194

Subproblem 2

x + -0.1020833334 = -2.468553086 Simplifying x + -0.1020833334 = -2.468553086 Reorder the terms: -0.1020833334 + x = -2.468553086 Solving -0.1020833334 + x = -2.468553086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1020833334' to each side of the equation. -0.1020833334 + 0.1020833334 + x = -2.468553086 + 0.1020833334 Combine like terms: -0.1020833334 + 0.1020833334 = 0.0000000000 0.0000000000 + x = -2.468553086 + 0.1020833334 x = -2.468553086 + 0.1020833334 Combine like terms: -2.468553086 + 0.1020833334 = -2.3664697526 x = -2.3664697526 Simplifying x = -2.3664697526

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.5706364194, -2.3664697526}

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