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Simplifying 0.5x2 + 2x + 1.5 = 0 Reorder the terms: 1.5 + 2x + 0.5x2 = 0 Solving 1.5 + 2x + 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'. 3 + 4x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 4x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 4x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x + x2 = 0 + -3 4x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 4x + x2 = -3 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -3 + 4 Reorder the terms: 4 + 4x + x2 = -3 + 4 Combine like terms: -3 + 4 = 1 4 + 4x + x2 = 1 Factor a perfect square on the left side: (x + 2)(x + 2) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + 2) equal to 1 and -1.Subproblem 1
x + 2 = 1 Simplifying x + 2 = 1 Reorder the terms: 2 + x = 1 Solving 2 + x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1 + -2 x = 1 + -2 Combine like terms: 1 + -2 = -1 x = -1 Simplifying x = -1Subproblem 2
x + 2 = -1 Simplifying x + 2 = -1 Reorder the terms: 2 + x = -1 Solving 2 + x = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1 + -2 x = -1 + -2 Combine like terms: -1 + -2 = -3 x = -3 Simplifying x = -3Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1, -3}
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