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Simplifying 0.25x2 + -4x + -20 = 0 Reorder the terms: -20 + -4x + 0.25x2 = 0 Solving -20 + -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'. -80 + -16x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + -16x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -16x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -16x + x2 = 0 + 80 -16x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -16x + x2 = 80 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 = 80 + 64 Reorder the terms: 64 + -16x + x2 = 80 + 64 Combine like terms: 80 + 64 = 144 64 + -16x + x2 = 144 Factor a perfect square on the left side: (x + -8)(x + -8) = 144 Calculate the square root of the right side: 12 Break this problem into two subproblems by setting (x + -8) equal to 12 and -12.Subproblem 1
x + -8 = 12 Simplifying x + -8 = 12 Reorder the terms: -8 + x = 12 Solving -8 + x = 12 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 = 12 + 8 Combine like terms: -8 + 8 = 0 0 + x = 12 + 8 x = 12 + 8 Combine like terms: 12 + 8 = 20 x = 20 Simplifying x = 20Subproblem 2
x + -8 = -12 Simplifying x + -8 = -12 Reorder the terms: -8 + x = -12 Solving -8 + x = -12 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 = -12 + 8 Combine like terms: -8 + 8 = 0 0 + x = -12 + 8 x = -12 + 8 Combine like terms: -12 + 8 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -4}
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