10x-3x(8-5x)=74

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Solution for 10x-3x(8-5x)=74 equation:


Simplifying
10x + -3x(8 + -5x) = 74
10x + (8 * -3x + -5x * -3x) = 74
10x + (-24x + 15x2) = 74

Combine like terms: 10x + -24x = -14x
-14x + 15x2 = 74

Solving
-14x + 15x2 = 74

Solving for variable 'x'.

Reorder the terms:
-74 + -14x + 15x2 = 74 + -74

Combine like terms: 74 + -74 = 0
-74 + -14x + 15x2 = 0

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

Divide each side by '15'.
-4.933333333 + -0.9333333333x + x2 = 0

Move the constant term to the right:

Add '4.933333333' to each side of the equation.
-4.933333333 + -0.9333333333x + 4.933333333 + x2 = 0 + 4.933333333

Reorder the terms:
-4.933333333 + 4.933333333 + -0.9333333333x + x2 = 0 + 4.933333333

Combine like terms: -4.933333333 + 4.933333333 = 0.000000000
0.000000000 + -0.9333333333x + x2 = 0 + 4.933333333
-0.9333333333x + x2 = 0 + 4.933333333

Combine like terms: 0 + 4.933333333 = 4.933333333
-0.9333333333x + x2 = 4.933333333

The x term is -0.9333333333x.  Take half its coefficient (-0.4666666667).
Square it (0.2177777778) and add it to both sides.

Add '0.2177777778' to each side of the equation.
-0.9333333333x + 0.2177777778 + x2 = 4.933333333 + 0.2177777778

Reorder the terms:
0.2177777778 + -0.9333333333x + x2 = 4.933333333 + 0.2177777778

Combine like terms: 4.933333333 + 0.2177777778 = 5.1511111108
0.2177777778 + -0.9333333333x + x2 = 5.1511111108

Factor a perfect square on the left side:
(x + -0.4666666667)(x + -0.4666666667) = 5.1511111108

Calculate the square root of the right side: 2.269605937

Break this problem into two subproblems by setting 
(x + -0.4666666667) equal to 2.269605937 and -2.269605937.

Subproblem 1

x + -0.4666666667 = 2.269605937 Simplifying x + -0.4666666667 = 2.269605937 Reorder the terms: -0.4666666667 + x = 2.269605937 Solving -0.4666666667 + x = 2.269605937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4666666667' to each side of the equation. -0.4666666667 + 0.4666666667 + x = 2.269605937 + 0.4666666667 Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000 0.0000000000 + x = 2.269605937 + 0.4666666667 x = 2.269605937 + 0.4666666667 Combine like terms: 2.269605937 + 0.4666666667 = 2.7362726037 x = 2.7362726037 Simplifying x = 2.7362726037

Subproblem 2

x + -0.4666666667 = -2.269605937 Simplifying x + -0.4666666667 = -2.269605937 Reorder the terms: -0.4666666667 + x = -2.269605937 Solving -0.4666666667 + x = -2.269605937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4666666667' to each side of the equation. -0.4666666667 + 0.4666666667 + x = -2.269605937 + 0.4666666667 Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000 0.0000000000 + x = -2.269605937 + 0.4666666667 x = -2.269605937 + 0.4666666667 Combine like terms: -2.269605937 + 0.4666666667 = -1.8029392703 x = -1.8029392703 Simplifying x = -1.8029392703

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.7362726037, -1.8029392703}

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