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Simplifying 0 = 0.25x2 + 2x + -5 Reorder the terms: 0 = -5 + 2x + 0.25x2 Solving 0 = -5 + 2x + 0.25x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + -2x + -0.25x2 = -5 + 2x + 0.25x2 + 5 + -2x + -0.25x2 Reorder the terms: 5 + -2x + -0.25x2 = -5 + 5 + 2x + -2x + 0.25x2 + -0.25x2 Combine like terms: -5 + 5 = 0 5 + -2x + -0.25x2 = 0 + 2x + -2x + 0.25x2 + -0.25x2 5 + -2x + -0.25x2 = 2x + -2x + 0.25x2 + -0.25x2 Combine like terms: 2x + -2x = 0 5 + -2x + -0.25x2 = 0 + 0.25x2 + -0.25x2 5 + -2x + -0.25x2 = 0.25x2 + -0.25x2 Combine like terms: 0.25x2 + -0.25x2 = 0.00 5 + -2x + -0.25x2 = 0.00 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -20 + 8x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 8x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 8x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 8x + x2 = 0 + 20 8x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 8x + x2 = 20 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 20 + 16 Reorder the terms: 16 + 8x + x2 = 20 + 16 Combine like terms: 20 + 16 = 36 16 + 8x + x2 = 36 Factor a perfect square on the left side: (x + 4)(x + 4) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + 4) equal to 6 and -6.Subproblem 1
x + 4 = 6 Simplifying x + 4 = 6 Reorder the terms: 4 + x = 6 Solving 4 + x = 6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 6 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6 + -4 x = 6 + -4 Combine like terms: 6 + -4 = 2 x = 2 Simplifying x = 2Subproblem 2
x + 4 = -6 Simplifying x + 4 = -6 Reorder the terms: 4 + x = -6 Solving 4 + x = -6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -6 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6 + -4 x = -6 + -4 Combine like terms: -6 + -4 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -10}
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