7x*7x+10x=360

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Solution for 7x*7x+10x=360 equation:


Simplifying
7x * 7x + 10x = 360

Reorder the terms for easier multiplication:
7 * 7x * x + 10x = 360

Multiply 7 * 7
49x * x + 10x = 360

Multiply x * x
49x2 + 10x = 360

Reorder the terms:
10x + 49x2 = 360

Solving
10x + 49x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 10x + 49x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 10x + 49x2 = 0

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

Divide each side by '49'.
-7.346938776 + 0.2040816327x + x2 = 0

Move the constant term to the right:

Add '7.346938776' to each side of the equation.
-7.346938776 + 0.2040816327x + 7.346938776 + x2 = 0 + 7.346938776

Reorder the terms:
-7.346938776 + 7.346938776 + 0.2040816327x + x2 = 0 + 7.346938776

Combine like terms: -7.346938776 + 7.346938776 = 0.000000000
0.000000000 + 0.2040816327x + x2 = 0 + 7.346938776
0.2040816327x + x2 = 0 + 7.346938776

Combine like terms: 0 + 7.346938776 = 7.346938776
0.2040816327x + x2 = 7.346938776

The x term is 0.2040816327x.  Take half its coefficient (0.1020408164).
Square it (0.01041232821) and add it to both sides.

Add '0.01041232821' to each side of the equation.
0.2040816327x + 0.01041232821 + x2 = 7.346938776 + 0.01041232821

Reorder the terms:
0.01041232821 + 0.2040816327x + x2 = 7.346938776 + 0.01041232821

Combine like terms: 7.346938776 + 0.01041232821 = 7.35735110421
0.01041232821 + 0.2040816327x + x2 = 7.35735110421

Factor a perfect square on the left side:
(x + 0.1020408164)(x + 0.1020408164) = 7.35735110421

Calculate the square root of the right side: 2.712443751

Break this problem into two subproblems by setting 
(x + 0.1020408164) equal to 2.712443751 and -2.712443751.

Subproblem 1

x + 0.1020408164 = 2.712443751 Simplifying x + 0.1020408164 = 2.712443751 Reorder the terms: 0.1020408164 + x = 2.712443751 Solving 0.1020408164 + x = 2.712443751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1020408164' to each side of the equation. 0.1020408164 + -0.1020408164 + x = 2.712443751 + -0.1020408164 Combine like terms: 0.1020408164 + -0.1020408164 = 0.0000000000 0.0000000000 + x = 2.712443751 + -0.1020408164 x = 2.712443751 + -0.1020408164 Combine like terms: 2.712443751 + -0.1020408164 = 2.6104029346 x = 2.6104029346 Simplifying x = 2.6104029346

Subproblem 2

x + 0.1020408164 = -2.712443751 Simplifying x + 0.1020408164 = -2.712443751 Reorder the terms: 0.1020408164 + x = -2.712443751 Solving 0.1020408164 + x = -2.712443751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1020408164' to each side of the equation. 0.1020408164 + -0.1020408164 + x = -2.712443751 + -0.1020408164 Combine like terms: 0.1020408164 + -0.1020408164 = 0.0000000000 0.0000000000 + x = -2.712443751 + -0.1020408164 x = -2.712443751 + -0.1020408164 Combine like terms: -2.712443751 + -0.1020408164 = -2.8144845674 x = -2.8144845674 Simplifying x = -2.8144845674

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.6104029346, -2.8144845674}

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