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Simplifying 0.5X2 + -4X + 3.5 = 0 Reorder the terms: 3.5 + -4X + 0.5X2 = 0 Solving 3.5 + -4X + 0.5X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 7 + -8X + X2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -8X + -7 + X2 = 0 + -7 Reorder the terms: 7 + -7 + -8X + X2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8X + X2 = 0 + -7 -8X + X2 = 0 + -7 Combine like terms: 0 + -7 = -7 -8X + X2 = -7 The X term is -8X. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8X + 16 + X2 = -7 + 16 Reorder the terms: 16 + -8X + X2 = -7 + 16 Combine like terms: -7 + 16 = 9 16 + -8X + X2 = 9 Factor a perfect square on the left side: (X + -4)(X + -4) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (X + -4) equal to 3 and -3.Subproblem 1
X + -4 = 3 Simplifying X + -4 = 3 Reorder the terms: -4 + X = 3 Solving -4 + X = 3 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = 3 + 4 Combine like terms: -4 + 4 = 0 0 + X = 3 + 4 X = 3 + 4 Combine like terms: 3 + 4 = 7 X = 7 Simplifying X = 7Subproblem 2
X + -4 = -3 Simplifying X + -4 = -3 Reorder the terms: -4 + X = -3 Solving -4 + X = -3 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = -3 + 4 Combine like terms: -4 + 4 = 0 0 + X = -3 + 4 X = -3 + 4 Combine like terms: -3 + 4 = 1 X = 1 Simplifying X = 1Solution
The solution to the problem is based on the solutions from the subproblems. X = {7, 1}
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