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Simplifying 0.5x2 + 5.5x + -24 = 0 Reorder the terms: -24 + 5.5x + 0.5x2 = 0 Solving -24 + 5.5x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -48 + 11x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 11x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 11x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 11x + x2 = 0 + 48 11x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 11x + x2 = 48 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 48 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 48 + 30.25 Combine like terms: 48 + 30.25 = 78.25 30.25 + 11x + x2 = 78.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + 5.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x + 5.5 = 8.845903006 Simplifying x + 5.5 = 8.845903006 Reorder the terms: 5.5 + x = 8.845903006 Solving 5.5 + x = 8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 8.845903006 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 8.845903006 + -5.5 x = 8.845903006 + -5.5 Combine like terms: 8.845903006 + -5.5 = 3.345903006 x = 3.345903006 Simplifying x = 3.345903006Subproblem 2
x + 5.5 = -8.845903006 Simplifying x + 5.5 = -8.845903006 Reorder the terms: 5.5 + x = -8.845903006 Solving 5.5 + x = -8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -8.845903006 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -8.845903006 + -5.5 x = -8.845903006 + -5.5 Combine like terms: -8.845903006 + -5.5 = -14.345903006 x = -14.345903006 Simplifying x = -14.345903006Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.345903006, -14.345903006}
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