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Simplifying 0.25x2 + 0.5x + -6 = 0 Reorder the terms: -6 + 0.5x + 0.25x2 = 0 Solving -6 + 0.5x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -24 + 2x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 2x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 2x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 2x + x2 = 0 + 24 2x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 2x + x2 = 24 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 = 24 + 1 Reorder the terms: 1 + 2x + x2 = 24 + 1 Combine like terms: 24 + 1 = 25 1 + 2x + x2 = 25 Factor a perfect square on the left side: (x + 1)(x + 1) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + 1) equal to 5 and -5.Subproblem 1
x + 1 = 5 Simplifying x + 1 = 5 Reorder the terms: 1 + x = 5 Solving 1 + x = 5 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 = 5 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5 + -1 x = 5 + -1 Combine like terms: 5 + -1 = 4 x = 4 Simplifying x = 4Subproblem 2
x + 1 = -5 Simplifying x + 1 = -5 Reorder the terms: 1 + x = -5 Solving 1 + x = -5 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 = -5 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5 + -1 x = -5 + -1 Combine like terms: -5 + -1 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -6}
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