(40+2x)(60+2x)=248

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Solution for (40+2x)(60+2x)=248 equation:


Simplifying
(40 + 2x)(60 + 2x) = 248

Multiply (40 + 2x) * (60 + 2x)
(40(60 + 2x) + 2x * (60 + 2x)) = 248
((60 * 40 + 2x * 40) + 2x * (60 + 2x)) = 248
((2400 + 80x) + 2x * (60 + 2x)) = 248
(2400 + 80x + (60 * 2x + 2x * 2x)) = 248
(2400 + 80x + (120x + 4x2)) = 248

Combine like terms: 80x + 120x = 200x
(2400 + 200x + 4x2) = 248

Solving
2400 + 200x + 4x2 = 248

Solving for variable 'x'.

Reorder the terms:
2400 + -248 + 200x + 4x2 = 248 + -248

Combine like terms: 2400 + -248 = 2152
2152 + 200x + 4x2 = 248 + -248

Combine like terms: 248 + -248 = 0
2152 + 200x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(538 + 50x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(538 + 50x + x2)' equal to zero and attempt to solve: Simplifying 538 + 50x + x2 = 0 Solving 538 + 50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-538' to each side of the equation. 538 + 50x + -538 + x2 = 0 + -538 Reorder the terms: 538 + -538 + 50x + x2 = 0 + -538 Combine like terms: 538 + -538 = 0 0 + 50x + x2 = 0 + -538 50x + x2 = 0 + -538 Combine like terms: 0 + -538 = -538 50x + x2 = -538 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = -538 + 625 Reorder the terms: 625 + 50x + x2 = -538 + 625 Combine like terms: -538 + 625 = 87 625 + 50x + x2 = 87 Factor a perfect square on the left side: (x + 25)(x + 25) = 87 Calculate the square root of the right side: 9.327379053 Break this problem into two subproblems by setting (x + 25) equal to 9.327379053 and -9.327379053.

Subproblem 1

x + 25 = 9.327379053 Simplifying x + 25 = 9.327379053 Reorder the terms: 25 + x = 9.327379053 Solving 25 + x = 9.327379053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 9.327379053 + -25 Combine like terms: 25 + -25 = 0 0 + x = 9.327379053 + -25 x = 9.327379053 + -25 Combine like terms: 9.327379053 + -25 = -15.672620947 x = -15.672620947 Simplifying x = -15.672620947

Subproblem 2

x + 25 = -9.327379053 Simplifying x + 25 = -9.327379053 Reorder the terms: 25 + x = -9.327379053 Solving 25 + x = -9.327379053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -9.327379053 + -25 Combine like terms: 25 + -25 = 0 0 + x = -9.327379053 + -25 x = -9.327379053 + -25 Combine like terms: -9.327379053 + -25 = -34.327379053 x = -34.327379053 Simplifying x = -34.327379053

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-15.672620947, -34.327379053}

Solution

x = {-15.672620947, -34.327379053}

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