5x^2+10x=155

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Solution for 5x^2+10x=155 equation:


Simplifying
5x2 + 10x = 155

Reorder the terms:
10x + 5x2 = 155

Solving
10x + 5x2 = 155

Solving for variable 'x'.

Reorder the terms:
-155 + 10x + 5x2 = 155 + -155

Combine like terms: 155 + -155 = 0
-155 + 10x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-31 + 2x + x2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-31 + 2x + x2)' equal to zero and attempt to solve: Simplifying -31 + 2x + x2 = 0 Solving -31 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 2x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 2x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 2x + x2 = 0 + 31 2x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 2x + x2 = 31 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 31 + 1 Reorder the terms: 1 + 2x + x2 = 31 + 1 Combine like terms: 31 + 1 = 32 1 + 2x + x2 = 32 Factor a perfect square on the left side: (x + 1)(x + 1) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 1) equal to 5.656854249 and -5.656854249.

Subproblem 1

x + 1 = 5.656854249 Simplifying x + 1 = 5.656854249 Reorder the terms: 1 + x = 5.656854249 Solving 1 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.656854249 + -1 x = 5.656854249 + -1 Combine like terms: 5.656854249 + -1 = 4.656854249 x = 4.656854249 Simplifying x = 4.656854249

Subproblem 2

x + 1 = -5.656854249 Simplifying x + 1 = -5.656854249 Reorder the terms: 1 + x = -5.656854249 Solving 1 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.656854249 + -1 x = -5.656854249 + -1 Combine like terms: -5.656854249 + -1 = -6.656854249 x = -6.656854249 Simplifying x = -6.656854249

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.656854249, -6.656854249}

Solution

x = {4.656854249, -6.656854249}

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