2x^2+3=4x+7

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Solution for 2x^2+3=4x+7 equation:


Simplifying
2x2 + 3 = 4x + 7

Reorder the terms:
3 + 2x2 = 4x + 7

Reorder the terms:
3 + 2x2 = 7 + 4x

Solving
3 + 2x2 = 7 + 4x

Solving for variable 'x'.

Reorder the terms:
3 + -7 + -4x + 2x2 = 7 + 4x + -7 + -4x

Combine like terms: 3 + -7 = -4
-4 + -4x + 2x2 = 7 + 4x + -7 + -4x

Reorder the terms:
-4 + -4x + 2x2 = 7 + -7 + 4x + -4x

Combine like terms: 7 + -7 = 0
-4 + -4x + 2x2 = 0 + 4x + -4x
-4 + -4x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-4 + -4x + 2x2 = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + -2x + x2)' equal to zero and attempt to solve: Simplifying -2 + -2x + x2 = 0 Solving -2 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -2x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -2x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2x + x2 = 0 + 2 -2x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2x + x2 = 2 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 = 2 + 1 Reorder the terms: 1 + -2x + x2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2x + x2 = 3 Factor a perfect square on the left side: (x + -1)(x + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -1) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + -1 = 1.732050808 Simplifying x + -1 = 1.732050808 Reorder the terms: -1 + x = 1.732050808 Solving -1 + x = 1.732050808 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 = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.732050808 + 1 x = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 x = 2.732050808 Simplifying x = 2.732050808

Subproblem 2

x + -1 = -1.732050808 Simplifying x + -1 = -1.732050808 Reorder the terms: -1 + x = -1.732050808 Solving -1 + x = -1.732050808 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 = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.732050808 + 1 x = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 x = -0.732050808 Simplifying x = -0.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.732050808, -0.732050808}

Solution

x = {2.732050808, -0.732050808}

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