(2x-5)(2x-5)=7

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Solution for (2x-5)(2x-5)=7 equation:


Simplifying
(2x + -5)(2x + -5) = 7

Reorder the terms:
(-5 + 2x)(2x + -5) = 7

Reorder the terms:
(-5 + 2x)(-5 + 2x) = 7

Multiply (-5 + 2x) * (-5 + 2x)
(-5(-5 + 2x) + 2x * (-5 + 2x)) = 7
((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) = 7
((25 + -10x) + 2x * (-5 + 2x)) = 7
(25 + -10x + (-5 * 2x + 2x * 2x)) = 7
(25 + -10x + (-10x + 4x2)) = 7

Combine like terms: -10x + -10x = -20x
(25 + -20x + 4x2) = 7

Solving
25 + -20x + 4x2 = 7

Solving for variable 'x'.

Reorder the terms:
25 + -7 + -20x + 4x2 = 7 + -7

Combine like terms: 25 + -7 = 18
18 + -20x + 4x2 = 7 + -7

Combine like terms: 7 + -7 = 0
18 + -20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -10x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(9 + -10x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + -10x + 2x2 = 0 Solving 9 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -5x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -5x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -5x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -5x + x2 = 0 + -4.5 -5x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -5x + x2 = -4.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -4.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -4.5 + 6.25 Combine like terms: -4.5 + 6.25 = 1.75 6.25 + -5x + x2 = 1.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + -2.5) equal to 1.322875656 and -1.322875656.

Subproblem 1

x + -2.5 = 1.322875656 Simplifying x + -2.5 = 1.322875656 Reorder the terms: -2.5 + x = 1.322875656 Solving -2.5 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.322875656 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.322875656 + 2.5 x = 1.322875656 + 2.5 Combine like terms: 1.322875656 + 2.5 = 3.822875656 x = 3.822875656 Simplifying x = 3.822875656

Subproblem 2

x + -2.5 = -1.322875656 Simplifying x + -2.5 = -1.322875656 Reorder the terms: -2.5 + x = -1.322875656 Solving -2.5 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.322875656 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.322875656 + 2.5 x = -1.322875656 + 2.5 Combine like terms: -1.322875656 + 2.5 = 1.177124344 x = 1.177124344 Simplifying x = 1.177124344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.822875656, 1.177124344}

Solution

x = {3.822875656, 1.177124344}

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