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Simplifying 0 = -0.5x2 + 1.5x + 3.99 Reorder the terms: 0 = 3.99 + 1.5x + -0.5x2 Solving 0 = 3.99 + 1.5x + -0.5x2 Solving for variable 'x'. Combine like terms: 0 + -3.99 = -3.99 -3.99 + -1.5x + 0.5x2 = 3.99 + 1.5x + -0.5x2 + -3.99 + -1.5x + 0.5x2 Reorder the terms: -3.99 + -1.5x + 0.5x2 = 3.99 + -3.99 + 1.5x + -1.5x + -0.5x2 + 0.5x2 Combine like terms: 3.99 + -3.99 = 0.00 -3.99 + -1.5x + 0.5x2 = 0.00 + 1.5x + -1.5x + -0.5x2 + 0.5x2 -3.99 + -1.5x + 0.5x2 = 1.5x + -1.5x + -0.5x2 + 0.5x2 Combine like terms: 1.5x + -1.5x = 0.0 -3.99 + -1.5x + 0.5x2 = 0.0 + -0.5x2 + 0.5x2 -3.99 + -1.5x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -3.99 + -1.5x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -7.98 + -3x + x2 = 0 Move the constant term to the right: Add '7.98' to each side of the equation. -7.98 + -3x + 7.98 + x2 = 0 + 7.98 Reorder the terms: -7.98 + 7.98 + -3x + x2 = 0 + 7.98 Combine like terms: -7.98 + 7.98 = 0.00 0.00 + -3x + x2 = 0 + 7.98 -3x + x2 = 0 + 7.98 Combine like terms: 0 + 7.98 = 7.98 -3x + x2 = 7.98 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 7.98 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 7.98 + 2.25 Combine like terms: 7.98 + 2.25 = 10.23 2.25 + -3x + x2 = 10.23 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 10.23 Calculate the square root of the right side: 3.198437118 Break this problem into two subproblems by setting (x + -1.5) equal to 3.198437118 and -3.198437118.Subproblem 1
x + -1.5 = 3.198437118 Simplifying x + -1.5 = 3.198437118 Reorder the terms: -1.5 + x = 3.198437118 Solving -1.5 + x = 3.198437118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.198437118 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.198437118 + 1.5 x = 3.198437118 + 1.5 Combine like terms: 3.198437118 + 1.5 = 4.698437118 x = 4.698437118 Simplifying x = 4.698437118Subproblem 2
x + -1.5 = -3.198437118 Simplifying x + -1.5 = -3.198437118 Reorder the terms: -1.5 + x = -3.198437118 Solving -1.5 + x = -3.198437118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.198437118 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.198437118 + 1.5 x = -3.198437118 + 1.5 Combine like terms: -3.198437118 + 1.5 = -1.698437118 x = -1.698437118 Simplifying x = -1.698437118Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.698437118, -1.698437118}
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