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Simplifying 0.5x2 + -0.5x = 741 Reorder the terms: -0.5x + 0.5x2 = 741 Solving -0.5x + 0.5x2 = 741 Solving for variable 'x'. Reorder the terms: -741 + -0.5x + 0.5x2 = 741 + -741 Combine like terms: 741 + -741 = 0 -741 + -0.5x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -1482 + -1x + x2 = 0 Move the constant term to the right: Add '1482' to each side of the equation. -1482 + -1x + 1482 + x2 = 0 + 1482 Reorder the terms: -1482 + 1482 + -1x + x2 = 0 + 1482 Combine like terms: -1482 + 1482 = 0 0 + -1x + x2 = 0 + 1482 -1x + x2 = 0 + 1482 Combine like terms: 0 + 1482 = 1482 -1x + x2 = 1482 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 = 1482 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1482 + 0.25 Combine like terms: 1482 + 0.25 = 1482.25 0.25 + -1x + x2 = 1482.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1482.25 Calculate the square root of the right side: 38.5 Break this problem into two subproblems by setting (x + -0.5) equal to 38.5 and -38.5.Subproblem 1
x + -0.5 = 38.5 Simplifying x + -0.5 = 38.5 Reorder the terms: -0.5 + x = 38.5 Solving -0.5 + x = 38.5 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 = 38.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 38.5 + 0.5 x = 38.5 + 0.5 Combine like terms: 38.5 + 0.5 = 39 x = 39 Simplifying x = 39Subproblem 2
x + -0.5 = -38.5 Simplifying x + -0.5 = -38.5 Reorder the terms: -0.5 + x = -38.5 Solving -0.5 + x = -38.5 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 = -38.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -38.5 + 0.5 x = -38.5 + 0.5 Combine like terms: -38.5 + 0.5 = -38 x = -38 Simplifying x = -38Solution
The solution to the problem is based on the solutions from the subproblems. x = {39, -38}
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