7x^2+56x=49

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Solution for 7x^2+56x=49 equation:


Simplifying
7x2 + 56x = 49

Reorder the terms:
56x + 7x2 = 49

Solving
56x + 7x2 = 49

Solving for variable 'x'.

Reorder the terms:
-49 + 56x + 7x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + 56x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-7 + 8x + x2) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(-7 + 8x + x2)' equal to zero and attempt to solve: Simplifying -7 + 8x + x2 = 0 Solving -7 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 8x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 8x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 8x + x2 = 0 + 7 8x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 8x + x2 = 7 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 7 + 16 Reorder the terms: 16 + 8x + x2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + 8x + x2 = 23 Factor a perfect square on the left side: (x + 4)(x + 4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 4) equal to 4.795831523 and -4.795831523.

Subproblem 1

x + 4 = 4.795831523 Simplifying x + 4 = 4.795831523 Reorder the terms: 4 + x = 4.795831523 Solving 4 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.795831523 + -4 x = 4.795831523 + -4 Combine like terms: 4.795831523 + -4 = 0.795831523 x = 0.795831523 Simplifying x = 0.795831523

Subproblem 2

x + 4 = -4.795831523 Simplifying x + 4 = -4.795831523 Reorder the terms: 4 + x = -4.795831523 Solving 4 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.795831523 + -4 x = -4.795831523 + -4 Combine like terms: -4.795831523 + -4 = -8.795831523 x = -8.795831523 Simplifying x = -8.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.795831523, -8.795831523}

Solution

x = {0.795831523, -8.795831523}

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