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Simplifying 0.25x2 + -4x + 12 = 0 Reorder the terms: 12 + -4x + 0.25x2 = 0 Solving 12 + -4x + 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'. 48 + -16x + x2 = 0 Move the constant term to the right: Add '-48' to each side of the equation. 48 + -16x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + -16x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -16x + x2 = 0 + -48 -16x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 -16x + x2 = -48 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -48 + 64 Reorder the terms: 64 + -16x + x2 = -48 + 64 Combine like terms: -48 + 64 = 16 64 + -16x + x2 = 16 Factor a perfect square on the left side: (x + -8)(x + -8) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + -8) equal to 4 and -4.Subproblem 1
x + -8 = 4 Simplifying x + -8 = 4 Reorder the terms: -8 + x = 4 Solving -8 + x = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 4 + 8 Combine like terms: -8 + 8 = 0 0 + x = 4 + 8 x = 4 + 8 Combine like terms: 4 + 8 = 12 x = 12 Simplifying x = 12Subproblem 2
x + -8 = -4 Simplifying x + -8 = -4 Reorder the terms: -8 + x = -4 Solving -8 + x = -4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -4 + 8 Combine like terms: -8 + 8 = 0 0 + x = -4 + 8 x = -4 + 8 Combine like terms: -4 + 8 = 4 x = 4 Simplifying x = 4Solution
The solution to the problem is based on the solutions from the subproblems. x = {12, 4}
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