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Simplifying 0.25x2 + -1x + -48 = 0 Reorder the terms: -48 + -1x + 0.25x2 = 0 Solving -48 + -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'. -192 + -4x + x2 = 0 Move the constant term to the right: Add '192' to each side of the equation. -192 + -4x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + -4x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + -4x + x2 = 0 + 192 -4x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 -4x + x2 = 192 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 = 192 + 4 Reorder the terms: 4 + -4x + x2 = 192 + 4 Combine like terms: 192 + 4 = 196 4 + -4x + x2 = 196 Factor a perfect square on the left side: (x + -2)(x + -2) = 196 Calculate the square root of the right side: 14 Break this problem into two subproblems by setting (x + -2) equal to 14 and -14.Subproblem 1
x + -2 = 14 Simplifying x + -2 = 14 Reorder the terms: -2 + x = 14 Solving -2 + x = 14 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 = 14 + 2 Combine like terms: -2 + 2 = 0 0 + x = 14 + 2 x = 14 + 2 Combine like terms: 14 + 2 = 16 x = 16 Simplifying x = 16Subproblem 2
x + -2 = -14 Simplifying x + -2 = -14 Reorder the terms: -2 + x = -14 Solving -2 + x = -14 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 = -14 + 2 Combine like terms: -2 + 2 = 0 0 + x = -14 + 2 x = -14 + 2 Combine like terms: -14 + 2 = -12 x = -12 Simplifying x = -12Solution
The solution to the problem is based on the solutions from the subproblems. x = {16, -12}
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