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Simplifying 0.5x2 + -5x = 12 Reorder the terms: -5x + 0.5x2 = 12 Solving -5x + 0.5x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -5x + 0.5x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -5x + 0.5x2 = 0 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 = 12 x = 12 Simplifying x = 12Subproblem 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 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {12, -2}
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