(24-2x)(20-2x)=340

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Solution for (24-2x)(20-2x)=340 equation:


Simplifying
(24 + -2x)(20 + -2x) = 340

Multiply (24 + -2x) * (20 + -2x)
(24(20 + -2x) + -2x * (20 + -2x)) = 340
((20 * 24 + -2x * 24) + -2x * (20 + -2x)) = 340
((480 + -48x) + -2x * (20 + -2x)) = 340
(480 + -48x + (20 * -2x + -2x * -2x)) = 340
(480 + -48x + (-40x + 4x2)) = 340

Combine like terms: -48x + -40x = -88x
(480 + -88x + 4x2) = 340

Solving
480 + -88x + 4x2 = 340

Solving for variable 'x'.

Reorder the terms:
480 + -340 + -88x + 4x2 = 340 + -340

Combine like terms: 480 + -340 = 140
140 + -88x + 4x2 = 340 + -340

Combine like terms: 340 + -340 = 0
140 + -88x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(35 + -22x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(35 + -22x + x2)' equal to zero and attempt to solve: Simplifying 35 + -22x + x2 = 0 Solving 35 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -22x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -22x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -22x + x2 = 0 + -35 -22x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -22x + x2 = -35 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -35 + 121 Reorder the terms: 121 + -22x + x2 = -35 + 121 Combine like terms: -35 + 121 = 86 121 + -22x + x2 = 86 Factor a perfect square on the left side: (x + -11)(x + -11) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + -11) equal to 9.273618495 and -9.273618495.

Subproblem 1

x + -11 = 9.273618495 Simplifying x + -11 = 9.273618495 Reorder the terms: -11 + x = 9.273618495 Solving -11 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 9.273618495 + 11 Combine like terms: -11 + 11 = 0 0 + x = 9.273618495 + 11 x = 9.273618495 + 11 Combine like terms: 9.273618495 + 11 = 20.273618495 x = 20.273618495 Simplifying x = 20.273618495

Subproblem 2

x + -11 = -9.273618495 Simplifying x + -11 = -9.273618495 Reorder the terms: -11 + x = -9.273618495 Solving -11 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -9.273618495 + 11 Combine like terms: -11 + 11 = 0 0 + x = -9.273618495 + 11 x = -9.273618495 + 11 Combine like terms: -9.273618495 + 11 = 1.726381505 x = 1.726381505 Simplifying x = 1.726381505

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.273618495, 1.726381505}

Solution

x = {20.273618495, 1.726381505}

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