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Simplifying 0 = -0.25x2 + -0.5x + 0.75 Reorder the terms: 0 = 0.75 + -0.5x + -0.25x2 Solving 0 = 0.75 + -0.5x + -0.25x2 Solving for variable 'x'. Combine like terms: 0 + -0.75 = -0.75 -0.75 + 0.5x + 0.25x2 = 0.75 + -0.5x + -0.25x2 + -0.75 + 0.5x + 0.25x2 Reorder the terms: -0.75 + 0.5x + 0.25x2 = 0.75 + -0.75 + -0.5x + 0.5x + -0.25x2 + 0.25x2 Combine like terms: 0.75 + -0.75 = 0.00 -0.75 + 0.5x + 0.25x2 = 0.00 + -0.5x + 0.5x + -0.25x2 + 0.25x2 -0.75 + 0.5x + 0.25x2 = -0.5x + 0.5x + -0.25x2 + 0.25x2 Combine like terms: -0.5x + 0.5x = 0.0 -0.75 + 0.5x + 0.25x2 = 0.0 + -0.25x2 + 0.25x2 -0.75 + 0.5x + 0.25x2 = -0.25x2 + 0.25x2 Combine like terms: -0.25x2 + 0.25x2 = 0.00 -0.75 + 0.5x + 0.25x2 = 0.00 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -3 + 2x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x + x2 = 0 + 3 2x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2x + x2 = 3 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 3 + 1 Reorder the terms: 1 + 2x + x2 = 3 + 1 Combine like terms: 3 + 1 = 4 1 + 2x + x2 = 4 Factor a perfect square on the left side: (x + 1)(x + 1) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + 1) equal to 2 and -2.Subproblem 1
x + 1 = 2 Simplifying x + 1 = 2 Reorder the terms: 1 + x = 2 Solving 1 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2 + -1 x = 2 + -1 Combine like terms: 2 + -1 = 1 x = 1 Simplifying x = 1Subproblem 2
x + 1 = -2 Simplifying x + 1 = -2 Reorder the terms: 1 + x = -2 Solving 1 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2 + -1 x = -2 + -1 Combine like terms: -2 + -1 = -3 x = -3 Simplifying x = -3Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, -3}
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