7x^2-63=49x

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Solution for 7x^2-63=49x equation:


Simplifying
7x2 + -63 = 49x

Reorder the terms:
-63 + 7x2 = 49x

Solving
-63 + 7x2 = 49x

Solving for variable 'x'.

Reorder the terms:
-63 + -49x + 7x2 = 49x + -49x

Combine like terms: 49x + -49x = 0
-63 + -49x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-9 + -7x + x2) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(-9 + -7x + x2)' equal to zero and attempt to solve: Simplifying -9 + -7x + x2 = 0 Solving -9 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -7x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -7x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -7x + x2 = 0 + 9 -7x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -7x + x2 = 9 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 9 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 9 + 12.25 Combine like terms: 9 + 12.25 = 21.25 12.25 + -7x + x2 = 21.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + -3.5) equal to 4.609772229 and -4.609772229.

Subproblem 1

x + -3.5 = 4.609772229 Simplifying x + -3.5 = 4.609772229 Reorder the terms: -3.5 + x = 4.609772229 Solving -3.5 + x = 4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.609772229 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.609772229 + 3.5 x = 4.609772229 + 3.5 Combine like terms: 4.609772229 + 3.5 = 8.109772229 x = 8.109772229 Simplifying x = 8.109772229

Subproblem 2

x + -3.5 = -4.609772229 Simplifying x + -3.5 = -4.609772229 Reorder the terms: -3.5 + x = -4.609772229 Solving -3.5 + x = -4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.609772229 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.609772229 + 3.5 x = -4.609772229 + 3.5 Combine like terms: -4.609772229 + 3.5 = -1.109772229 x = -1.109772229 Simplifying x = -1.109772229

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.109772229, -1.109772229}

Solution

x = {8.109772229, -1.109772229}

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