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Simplifying 5X2 + 3X = 105 Reorder the terms: 3X + 5X2 = 105 Solving 3X + 5X2 = 105 Solving for variable 'X'. Reorder the terms: -105 + 3X + 5X2 = 105 + -105 Combine like terms: 105 + -105 = 0 -105 + 3X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -21 + 0.6X + X2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 0.6X + 21 + X2 = 0 + 21 Reorder the terms: -21 + 21 + 0.6X + X2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 0.6X + X2 = 0 + 21 0.6X + X2 = 0 + 21 Combine like terms: 0 + 21 = 21 0.6X + X2 = 21 The X term is 0.6X. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6X + 0.09 + X2 = 21 + 0.09 Reorder the terms: 0.09 + 0.6X + X2 = 21 + 0.09 Combine like terms: 21 + 0.09 = 21.09 0.09 + 0.6X + X2 = 21.09 Factor a perfect square on the left side: (X + 0.3)(X + 0.3) = 21.09 Calculate the square root of the right side: 4.592385001 Break this problem into two subproblems by setting (X + 0.3) equal to 4.592385001 and -4.592385001.Subproblem 1
X + 0.3 = 4.592385001 Simplifying X + 0.3 = 4.592385001 Reorder the terms: 0.3 + X = 4.592385001 Solving 0.3 + X = 4.592385001 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + X = 4.592385001 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + X = 4.592385001 + -0.3 X = 4.592385001 + -0.3 Combine like terms: 4.592385001 + -0.3 = 4.292385001 X = 4.292385001 Simplifying X = 4.292385001Subproblem 2
X + 0.3 = -4.592385001 Simplifying X + 0.3 = -4.592385001 Reorder the terms: 0.3 + X = -4.592385001 Solving 0.3 + X = -4.592385001 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + X = -4.592385001 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + X = -4.592385001 + -0.3 X = -4.592385001 + -0.3 Combine like terms: -4.592385001 + -0.3 = -4.892385001 X = -4.892385001 Simplifying X = -4.892385001Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.292385001, -4.892385001}
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