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Simplifying 0.25x2 + -3x + 8 = 0 Reorder the terms: 8 + -3x + 0.25x2 = 0 Solving 8 + -3x + 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'. 32 + -12x + x2 = 0 Move the constant term to the right: Add '-32' to each side of the equation. 32 + -12x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + -12x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -12x + x2 = 0 + -32 -12x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 -12x + x2 = -32 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -32 + 36 Reorder the terms: 36 + -12x + x2 = -32 + 36 Combine like terms: -32 + 36 = 4 36 + -12x + x2 = 4 Factor a perfect square on the left side: (x + -6)(x + -6) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -6) equal to 2 and -2.Subproblem 1
x + -6 = 2 Simplifying x + -6 = 2 Reorder the terms: -6 + x = 2 Solving -6 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 2 + 6 Combine like terms: -6 + 6 = 0 0 + x = 2 + 6 x = 2 + 6 Combine like terms: 2 + 6 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -6 = -2 Simplifying x + -6 = -2 Reorder the terms: -6 + x = -2 Solving -6 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -2 + 6 Combine like terms: -6 + 6 = 0 0 + x = -2 + 6 x = -2 + 6 Combine like terms: -2 + 6 = 4 x = 4 Simplifying x = 4Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, 4}
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