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Simplifying 0.5x2 + 3x + 4 = 0 Reorder the terms: 4 + 3x + 0.5x2 = 0 Solving 4 + 3x + 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'. 8 + 6x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 6x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 6x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 6x + x2 = 0 + -8 6x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 6x + x2 = -8 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 = -8 + 9 Reorder the terms: 9 + 6x + x2 = -8 + 9 Combine like terms: -8 + 9 = 1 9 + 6x + x2 = 1 Factor a perfect square on the left side: (x + 3)(x + 3) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + 3) equal to 1 and -1.Subproblem 1
x + 3 = 1 Simplifying x + 3 = 1 Reorder the terms: 3 + x = 1 Solving 3 + x = 1 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 = 1 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1 + -3 x = 1 + -3 Combine like terms: 1 + -3 = -2 x = -2 Simplifying x = -2Subproblem 2
x + 3 = -1 Simplifying x + 3 = -1 Reorder the terms: 3 + x = -1 Solving 3 + x = -1 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 = -1 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1 + -3 x = -1 + -3 Combine like terms: -1 + -3 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2, -4}
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