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Simplifying (60 + -2x)(50 + -2x) + -2400 = 0 Multiply (60 + -2x) * (50 + -2x) (60(50 + -2x) + -2x * (50 + -2x)) + -2400 = 0 ((50 * 60 + -2x * 60) + -2x * (50 + -2x)) + -2400 = 0 ((3000 + -120x) + -2x * (50 + -2x)) + -2400 = 0 (3000 + -120x + (50 * -2x + -2x * -2x)) + -2400 = 0 (3000 + -120x + (-100x + 4x2)) + -2400 = 0 Combine like terms: -120x + -100x = -220x (3000 + -220x + 4x2) + -2400 = 0 Reorder the terms: 3000 + -2400 + -220x + 4x2 = 0 Combine like terms: 3000 + -2400 = 600 600 + -220x + 4x2 = 0 Solving 600 + -220x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(150 + -55x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(150 + -55x + x2)' equal to zero and attempt to solve: Simplifying 150 + -55x + x2 = 0 Solving 150 + -55x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-150' to each side of the equation. 150 + -55x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + -55x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -55x + x2 = 0 + -150 -55x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 -55x + x2 = -150 The x term is -55x. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55x + 756.25 + x2 = -150 + 756.25 Reorder the terms: 756.25 + -55x + x2 = -150 + 756.25 Combine like terms: -150 + 756.25 = 606.25 756.25 + -55x + x2 = 606.25 Factor a perfect square on the left side: (x + -27.5)(x + -27.5) = 606.25 Calculate the square root of the right side: 24.622144504 Break this problem into two subproblems by setting (x + -27.5) equal to 24.622144504 and -24.622144504.Subproblem 1
x + -27.5 = 24.622144504 Simplifying x + -27.5 = 24.622144504 Reorder the terms: -27.5 + x = 24.622144504 Solving -27.5 + x = 24.622144504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = 24.622144504 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = 24.622144504 + 27.5 x = 24.622144504 + 27.5 Combine like terms: 24.622144504 + 27.5 = 52.122144504 x = 52.122144504 Simplifying x = 52.122144504Subproblem 2
x + -27.5 = -24.622144504 Simplifying x + -27.5 = -24.622144504 Reorder the terms: -27.5 + x = -24.622144504 Solving -27.5 + x = -24.622144504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = -24.622144504 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = -24.622144504 + 27.5 x = -24.622144504 + 27.5 Combine like terms: -24.622144504 + 27.5 = 2.877855496 x = 2.877855496 Simplifying x = 2.877855496Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.122144504, 2.877855496}Solution
x = {52.122144504, 2.877855496}
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