7x+5x(24-x)=147

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Solution for 7x+5x(24-x)=147 equation:


Simplifying
7x + 5x(24 + -1x) = 147
7x + (24 * 5x + -1x * 5x) = 147
7x + (120x + -5x2) = 147

Combine like terms: 7x + 120x = 127x
127x + -5x2 = 147

Solving
127x + -5x2 = 147

Solving for variable 'x'.

Reorder the terms:
-147 + 127x + -5x2 = 147 + -147

Combine like terms: 147 + -147 = 0
-147 + 127x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
29.4 + -25.4x + x2 = 0

Move the constant term to the right:

Add '-29.4' to each side of the equation.
29.4 + -25.4x + -29.4 + x2 = 0 + -29.4

Reorder the terms:
29.4 + -29.4 + -25.4x + x2 = 0 + -29.4

Combine like terms: 29.4 + -29.4 = 0.0
0.0 + -25.4x + x2 = 0 + -29.4
-25.4x + x2 = 0 + -29.4

Combine like terms: 0 + -29.4 = -29.4
-25.4x + x2 = -29.4

The x term is -25.4x.  Take half its coefficient (-12.7).
Square it (161.29) and add it to both sides.

Add '161.29' to each side of the equation.
-25.4x + 161.29 + x2 = -29.4 + 161.29

Reorder the terms:
161.29 + -25.4x + x2 = -29.4 + 161.29

Combine like terms: -29.4 + 161.29 = 131.89
161.29 + -25.4x + x2 = 131.89

Factor a perfect square on the left side:
(x + -12.7)(x + -12.7) = 131.89

Calculate the square root of the right side: 11.48433716

Break this problem into two subproblems by setting 
(x + -12.7) equal to 11.48433716 and -11.48433716.

Subproblem 1

x + -12.7 = 11.48433716 Simplifying x + -12.7 = 11.48433716 Reorder the terms: -12.7 + x = 11.48433716 Solving -12.7 + x = 11.48433716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.7' to each side of the equation. -12.7 + 12.7 + x = 11.48433716 + 12.7 Combine like terms: -12.7 + 12.7 = 0.0 0.0 + x = 11.48433716 + 12.7 x = 11.48433716 + 12.7 Combine like terms: 11.48433716 + 12.7 = 24.18433716 x = 24.18433716 Simplifying x = 24.18433716

Subproblem 2

x + -12.7 = -11.48433716 Simplifying x + -12.7 = -11.48433716 Reorder the terms: -12.7 + x = -11.48433716 Solving -12.7 + x = -11.48433716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.7' to each side of the equation. -12.7 + 12.7 + x = -11.48433716 + 12.7 Combine like terms: -12.7 + 12.7 = 0.0 0.0 + x = -11.48433716 + 12.7 x = -11.48433716 + 12.7 Combine like terms: -11.48433716 + 12.7 = 1.21566284 x = 1.21566284 Simplifying x = 1.21566284

Solution

The solution to the problem is based on the solutions from the subproblems. x = {24.18433716, 1.21566284}

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