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Simplifying 0.25x2 + -1x + -5 = 0 Reorder the terms: -5 + -1x + 0.25x2 = 0 Solving -5 + -1x + 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'. -20 + -4x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -4x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -4x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -4x + x2 = 0 + 20 -4x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -4x + x2 = 20 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 20 + 4 Reorder the terms: 4 + -4x + x2 = 20 + 4 Combine like terms: 20 + 4 = 24 4 + -4x + x2 = 24 Factor a perfect square on the left side: (x + -2)(x + -2) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -2) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -2 = 4.898979486 Simplifying x + -2 = 4.898979486 Reorder the terms: -2 + x = 4.898979486 Solving -2 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.898979486 + 2 x = 4.898979486 + 2 Combine like terms: 4.898979486 + 2 = 6.898979486 x = 6.898979486 Simplifying x = 6.898979486Subproblem 2
x + -2 = -4.898979486 Simplifying x + -2 = -4.898979486 Reorder the terms: -2 + x = -4.898979486 Solving -2 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.898979486 + 2 x = -4.898979486 + 2 Combine like terms: -4.898979486 + 2 = -2.898979486 x = -2.898979486 Simplifying x = -2.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.898979486, -2.898979486}
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