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Simplifying 0.5x2 + -7x + 12 = 0 Reorder the terms: 12 + -7x + 0.5x2 = 0 Solving 12 + -7x + 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 + -14x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -14x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -14x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -14x + x2 = 0 + -24 -14x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -14x + x2 = -24 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -24 + 49 Reorder the terms: 49 + -14x + x2 = -24 + 49 Combine like terms: -24 + 49 = 25 49 + -14x + x2 = 25 Factor a perfect square on the left side: (x + -7)(x + -7) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + -7) equal to 5 and -5.Subproblem 1
x + -7 = 5 Simplifying x + -7 = 5 Reorder the terms: -7 + x = 5 Solving -7 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 5 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5 + 7 x = 5 + 7 Combine like terms: 5 + 7 = 12 x = 12 Simplifying x = 12Subproblem 2
x + -7 = -5 Simplifying x + -7 = -5 Reorder the terms: -7 + x = -5 Solving -7 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -5 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5 + 7 x = -5 + 7 Combine like terms: -5 + 7 = 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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