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Simplifying -0.5x2 + 0.5x + 30.48 = 0 Reorder the terms: 30.48 + 0.5x + -0.5x2 = 0 Solving 30.48 + 0.5x + -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'. -60.96 + -1x + x2 = 0 Move the constant term to the right: Add '60.96' to each side of the equation. -60.96 + -1x + 60.96 + x2 = 0 + 60.96 Reorder the terms: -60.96 + 60.96 + -1x + x2 = 0 + 60.96 Combine like terms: -60.96 + 60.96 = 0.00 0.00 + -1x + x2 = 0 + 60.96 -1x + x2 = 0 + 60.96 Combine like terms: 0 + 60.96 = 60.96 -1x + x2 = 60.96 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 = 60.96 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 60.96 + 0.25 Combine like terms: 60.96 + 0.25 = 61.21 0.25 + -1x + x2 = 61.21 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 61.21 Calculate the square root of the right side: 7.823681998 Break this problem into two subproblems by setting (x + -0.5) equal to 7.823681998 and -7.823681998.Subproblem 1
x + -0.5 = 7.823681998 Simplifying x + -0.5 = 7.823681998 Reorder the terms: -0.5 + x = 7.823681998 Solving -0.5 + x = 7.823681998 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 = 7.823681998 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 7.823681998 + 0.5 x = 7.823681998 + 0.5 Combine like terms: 7.823681998 + 0.5 = 8.323681998 x = 8.323681998 Simplifying x = 8.323681998Subproblem 2
x + -0.5 = -7.823681998 Simplifying x + -0.5 = -7.823681998 Reorder the terms: -0.5 + x = -7.823681998 Solving -0.5 + x = -7.823681998 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 = -7.823681998 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -7.823681998 + 0.5 x = -7.823681998 + 0.5 Combine like terms: -7.823681998 + 0.5 = -7.323681998 x = -7.323681998 Simplifying x = -7.323681998Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.323681998, -7.323681998}
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