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Simplifying 0.5x + -0.5x2 = -3.38 Solving 0.5x + -0.5x2 = -3.38 Solving for variable 'x'. Reorder the terms: 3.38 + 0.5x + -0.5x2 = -3.38 + 3.38 Combine like terms: -3.38 + 3.38 = 0.00 3.38 + 0.5x + -0.5x2 = 0.00 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -6.76 + -1x + x2 = 0.0 Move the constant term to the right: Add '6.76' to each side of the equation. -6.76 + -1x + 6.76 + x2 = 0.0 + 6.76 Reorder the terms: -6.76 + 6.76 + -1x + x2 = 0.0 + 6.76 Combine like terms: -6.76 + 6.76 = 0.00 0.00 + -1x + x2 = 0.0 + 6.76 -1x + x2 = 0.0 + 6.76 Combine like terms: 0.0 + 6.76 = 6.76 -1x + x2 = 6.76 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 6.76 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 6.76 + 0.25 Combine like terms: 6.76 + 0.25 = 7.01 0.25 + -1x + x2 = 7.01 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 7.01 Calculate the square root of the right side: 2.647640459 Break this problem into two subproblems by setting (x + -0.5) equal to 2.647640459 and -2.647640459.Subproblem 1
x + -0.5 = 2.647640459 Simplifying x + -0.5 = 2.647640459 Reorder the terms: -0.5 + x = 2.647640459 Solving -0.5 + x = 2.647640459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.647640459 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.647640459 + 0.5 x = 2.647640459 + 0.5 Combine like terms: 2.647640459 + 0.5 = 3.147640459 x = 3.147640459 Simplifying x = 3.147640459Subproblem 2
x + -0.5 = -2.647640459 Simplifying x + -0.5 = -2.647640459 Reorder the terms: -0.5 + x = -2.647640459 Solving -0.5 + x = -2.647640459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.647640459 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.647640459 + 0.5 x = -2.647640459 + 0.5 Combine like terms: -2.647640459 + 0.5 = -2.147640459 x = -2.147640459 Simplifying x = -2.147640459Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.147640459, -2.147640459}
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