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Simplifying 0.5x2 + 5x + -12 = 0 Reorder the terms: -12 + 5x + 0.5x2 = 0 Solving -12 + 5x + 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'. -24 + 10x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 10x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 10x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 10x + x2 = 0 + 24 10x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 10x + x2 = 24 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 24 + 25 Reorder the terms: 25 + 10x + x2 = 24 + 25 Combine like terms: 24 + 25 = 49 25 + 10x + x2 = 49 Factor a perfect square on the left side: (x + 5)(x + 5) = 49 Calculate the square root of the right side: 7 Break this problem into two subproblems by setting (x + 5) equal to 7 and -7.Subproblem 1
x + 5 = 7 Simplifying x + 5 = 7 Reorder the terms: 5 + x = 7 Solving 5 + x = 7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 7 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7 + -5 x = 7 + -5 Combine like terms: 7 + -5 = 2 x = 2 Simplifying x = 2Subproblem 2
x + 5 = -7 Simplifying x + 5 = -7 Reorder the terms: 5 + x = -7 Solving 5 + x = -7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -7 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7 + -5 x = -7 + -5 Combine like terms: -7 + -5 = -12 x = -12 Simplifying x = -12Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -12}
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