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Simplifying 300 = 243.6x + -0.5x2 Solving 300 = 243.6x + -0.5x2 Solving for variable 'x'. Reorder the terms: 300 + -243.6x + 0.5x2 = 243.6x + -243.6x + -0.5x2 + 0.5x2 Combine like terms: 243.6x + -243.6x = 0.0 300 + -243.6x + 0.5x2 = 0.0 + -0.5x2 + 0.5x2 300 + -243.6x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 300 + -243.6x + 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'. 600 + -487.2x + x2 = 0 Move the constant term to the right: Add '-600' to each side of the equation. 600 + -487.2x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -487.2x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -487.2x + x2 = 0 + -600 -487.2x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -487.2x + x2 = -600 The x term is -487.2x. Take half its coefficient (-243.6). Square it (59340.96) and add it to both sides. Add '59340.96' to each side of the equation. -487.2x + 59340.96 + x2 = -600 + 59340.96 Reorder the terms: 59340.96 + -487.2x + x2 = -600 + 59340.96 Combine like terms: -600 + 59340.96 = 58740.96 59340.96 + -487.2x + x2 = 58740.96 Factor a perfect square on the left side: (x + -243.6)(x + -243.6) = 58740.96 Calculate the square root of the right side: 242.365344057 Break this problem into two subproblems by setting (x + -243.6) equal to 242.365344057 and -242.365344057.Subproblem 1
x + -243.6 = 242.365344057 Simplifying x + -243.6 = 242.365344057 Reorder the terms: -243.6 + x = 242.365344057 Solving -243.6 + x = 242.365344057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '243.6' to each side of the equation. -243.6 + 243.6 + x = 242.365344057 + 243.6 Combine like terms: -243.6 + 243.6 = 0.0 0.0 + x = 242.365344057 + 243.6 x = 242.365344057 + 243.6 Combine like terms: 242.365344057 + 243.6 = 485.965344057 x = 485.965344057 Simplifying x = 485.965344057Subproblem 2
x + -243.6 = -242.365344057 Simplifying x + -243.6 = -242.365344057 Reorder the terms: -243.6 + x = -242.365344057 Solving -243.6 + x = -242.365344057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '243.6' to each side of the equation. -243.6 + 243.6 + x = -242.365344057 + 243.6 Combine like terms: -243.6 + 243.6 = 0.0 0.0 + x = -242.365344057 + 243.6 x = -242.365344057 + 243.6 Combine like terms: -242.365344057 + 243.6 = 1.234655943 x = 1.234655943 Simplifying x = 1.234655943Solution
The solution to the problem is based on the solutions from the subproblems. x = {485.965344057, 1.234655943}
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