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Simplifying 2.7 = -0.5x2 + x + 4 Reorder the terms: 2.7 = 4 + x + -0.5x2 Solving 2.7 = 4 + x + -0.5x2 Solving for variable 'x'. Combine like terms: 2.7 + -4 = -1.3 -1.3 + -1x + 0.5x2 = 4 + x + -0.5x2 + -4 + -1x + 0.5x2 Reorder the terms: -1.3 + -1x + 0.5x2 = 4 + -4 + x + -1x + -0.5x2 + 0.5x2 Combine like terms: 4 + -4 = 0 -1.3 + -1x + 0.5x2 = 0 + x + -1x + -0.5x2 + 0.5x2 -1.3 + -1x + 0.5x2 = x + -1x + -0.5x2 + 0.5x2 Combine like terms: x + -1x = 0 -1.3 + -1x + 0.5x2 = 0 + -0.5x2 + 0.5x2 -1.3 + -1x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -1.3 + -1x + 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'. -2.6 + -2x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -2x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -2x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -2x + x2 = 0 + 2.6 -2x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -2x + x2 = 2.6 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 = 2.6 + 1 Reorder the terms: 1 + -2x + x2 = 2.6 + 1 Combine like terms: 2.6 + 1 = 3.6 1 + -2x + x2 = 3.6 Factor a perfect square on the left side: (x + -1)(x + -1) = 3.6 Calculate the square root of the right side: 1.897366596 Break this problem into two subproblems by setting (x + -1) equal to 1.897366596 and -1.897366596.Subproblem 1
x + -1 = 1.897366596 Simplifying x + -1 = 1.897366596 Reorder the terms: -1 + x = 1.897366596 Solving -1 + x = 1.897366596 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 = 1.897366596 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.897366596 + 1 x = 1.897366596 + 1 Combine like terms: 1.897366596 + 1 = 2.897366596 x = 2.897366596 Simplifying x = 2.897366596Subproblem 2
x + -1 = -1.897366596 Simplifying x + -1 = -1.897366596 Reorder the terms: -1 + x = -1.897366596 Solving -1 + x = -1.897366596 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 = -1.897366596 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.897366596 + 1 x = -1.897366596 + 1 Combine like terms: -1.897366596 + 1 = -0.897366596 x = -0.897366596 Simplifying x = -0.897366596Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.897366596, -0.897366596}
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