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Simplifying 0.5x2 + -1x + -24 = 0 Reorder the terms: -24 + -1x + 0.5x2 = 0 Solving -24 + -1x + 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'. -48 + -2x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + -2x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -2x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -2x + x2 = 0 + 48 -2x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -2x + x2 = 48 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 48 + 1 Reorder the terms: 1 + -2x + x2 = 48 + 1 Combine like terms: 48 + 1 = 49 1 + -2x + x2 = 49 Factor a perfect square on the left side: (x + -1)(x + -1) = 49 Calculate the square root of the right side: 7 Break this problem into two subproblems by setting (x + -1) equal to 7 and -7.Subproblem 1
x + -1 = 7 Simplifying x + -1 = 7 Reorder the terms: -1 + x = 7 Solving -1 + x = 7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 7 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7 + 1 x = 7 + 1 Combine like terms: 7 + 1 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -1 = -7 Simplifying x + -1 = -7 Reorder the terms: -1 + x = -7 Solving -1 + x = -7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -7 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7 + 1 x = -7 + 1 Combine like terms: -7 + 1 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -6}
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