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Simplifying 0.5X2 + 3X + -2 = 0.03 Reorder the terms: -2 + 3X + 0.5X2 = 0.03 Solving -2 + 3X + 0.5X2 = 0.03 Solving for variable 'X'. Reorder the terms: -2 + -0.03 + 3X + 0.5X2 = 0.03 + -0.03 Combine like terms: -2 + -0.03 = -2.03 -2.03 + 3X + 0.5X2 = 0.03 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 -2.03 + 3X + 0.5X2 = 0.00 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -4.06 + 6X + X2 = 0.0 Move the constant term to the right: Add '4.06' to each side of the equation. -4.06 + 6X + 4.06 + X2 = 0.0 + 4.06 Reorder the terms: -4.06 + 4.06 + 6X + X2 = 0.0 + 4.06 Combine like terms: -4.06 + 4.06 = 0.00 0.00 + 6X + X2 = 0.0 + 4.06 6X + X2 = 0.0 + 4.06 Combine like terms: 0.0 + 4.06 = 4.06 6X + X2 = 4.06 The X term is 6X. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6X + 9 + X2 = 4.06 + 9 Reorder the terms: 9 + 6X + X2 = 4.06 + 9 Combine like terms: 4.06 + 9 = 13.06 9 + 6X + X2 = 13.06 Factor a perfect square on the left side: (X + 3)(X + 3) = 13.06 Calculate the square root of the right side: 3.6138622 Break this problem into two subproblems by setting (X + 3) equal to 3.6138622 and -3.6138622.Subproblem 1
X + 3 = 3.6138622 Simplifying X + 3 = 3.6138622 Reorder the terms: 3 + X = 3.6138622 Solving 3 + X = 3.6138622 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = 3.6138622 + -3 Combine like terms: 3 + -3 = 0 0 + X = 3.6138622 + -3 X = 3.6138622 + -3 Combine like terms: 3.6138622 + -3 = 0.6138622 X = 0.6138622 Simplifying X = 0.6138622Subproblem 2
X + 3 = -3.6138622 Simplifying X + 3 = -3.6138622 Reorder the terms: 3 + X = -3.6138622 Solving 3 + X = -3.6138622 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = -3.6138622 + -3 Combine like terms: 3 + -3 = 0 0 + X = -3.6138622 + -3 X = -3.6138622 + -3 Combine like terms: -3.6138622 + -3 = -6.6138622 X = -6.6138622 Simplifying X = -6.6138622Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.6138622, -6.6138622}
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