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Simplifying 2X + 5X * 30X = 3020 Reorder the terms for easier multiplication: 2X + 5 * 30X * X = 3020 Multiply 5 * 30 2X + 150X * X = 3020 Multiply X * X 2X + 150X2 = 3020 Solving 2X + 150X2 = 3020 Solving for variable 'X'. Reorder the terms: -3020 + 2X + 150X2 = 3020 + -3020 Combine like terms: 3020 + -3020 = 0 -3020 + 2X + 150X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1510 + X + 75X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1510 + X + 75X2)' equal to zero and attempt to solve: Simplifying -1510 + X + 75X2 = 0 Solving -1510 + X + 75X2 = 0 Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. -20.13333333 + 0.01333333333X + X2 = 0 Move the constant term to the right: Add '20.13333333' to each side of the equation. -20.13333333 + 0.01333333333X + 20.13333333 + X2 = 0 + 20.13333333 Reorder the terms: -20.13333333 + 20.13333333 + 0.01333333333X + X2 = 0 + 20.13333333 Combine like terms: -20.13333333 + 20.13333333 = 0.00000000 0.00000000 + 0.01333333333X + X2 = 0 + 20.13333333 0.01333333333X + X2 = 0 + 20.13333333 Combine like terms: 0 + 20.13333333 = 20.13333333 0.01333333333X + X2 = 20.13333333 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.01333333333X + 0.25 + X2 = 20.13333333 + 0.25 Reorder the terms: 0.25 + 0.01333333333X + X2 = 20.13333333 + 0.25 Combine like terms: 20.13333333 + 0.25 = 20.38333333 0.25 + 0.01333333333X + X2 = 20.38333333 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 20.38333333 Calculate the square root of the right side: 4.514790508 Break this problem into two subproblems by setting (X + 0.5) equal to 4.514790508 and -4.514790508.Subproblem 1
X + 0.5 = 4.514790508 Simplifying X + 0.5 = 4.514790508 Reorder the terms: 0.5 + X = 4.514790508 Solving 0.5 + X = 4.514790508 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 4.514790508 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 4.514790508 + -0.5 X = 4.514790508 + -0.5 Combine like terms: 4.514790508 + -0.5 = 4.014790508 X = 4.014790508 Simplifying X = 4.014790508Subproblem 2
X + 0.5 = -4.514790508 Simplifying X + 0.5 = -4.514790508 Reorder the terms: 0.5 + X = -4.514790508 Solving 0.5 + X = -4.514790508 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -4.514790508 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -4.514790508 + -0.5 X = -4.514790508 + -0.5 Combine like terms: -4.514790508 + -0.5 = -5.014790508 X = -5.014790508 Simplifying X = -5.014790508Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.014790508, -5.014790508}Solution
X = {4.014790508, -5.014790508}
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