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Simplifying 0 = x2 + -243x + 4455 Reorder the terms: 0 = 4455 + -243x + x2 Solving 0 = 4455 + -243x + x2 Solving for variable 'x'. Combine like terms: 0 + -4455 = -4455 -4455 + 243x + -1x2 = 4455 + -243x + x2 + -4455 + 243x + -1x2 Reorder the terms: -4455 + 243x + -1x2 = 4455 + -4455 + -243x + 243x + x2 + -1x2 Combine like terms: 4455 + -4455 = 0 -4455 + 243x + -1x2 = 0 + -243x + 243x + x2 + -1x2 -4455 + 243x + -1x2 = -243x + 243x + x2 + -1x2 Combine like terms: -243x + 243x = 0 -4455 + 243x + -1x2 = 0 + x2 + -1x2 -4455 + 243x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4455 + 243x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4455 + -243x + x2 = 0 Move the constant term to the right: Add '-4455' to each side of the equation. 4455 + -243x + -4455 + x2 = 0 + -4455 Reorder the terms: 4455 + -4455 + -243x + x2 = 0 + -4455 Combine like terms: 4455 + -4455 = 0 0 + -243x + x2 = 0 + -4455 -243x + x2 = 0 + -4455 Combine like terms: 0 + -4455 = -4455 -243x + x2 = -4455 The x term is -243x. Take half its coefficient (-121.5). Square it (14762.25) and add it to both sides. Add '14762.25' to each side of the equation. -243x + 14762.25 + x2 = -4455 + 14762.25 Reorder the terms: 14762.25 + -243x + x2 = -4455 + 14762.25 Combine like terms: -4455 + 14762.25 = 10307.25 14762.25 + -243x + x2 = 10307.25 Factor a perfect square on the left side: (x + -121.5)(x + -121.5) = 10307.25 Calculate the square root of the right side: 101.524627554 Break this problem into two subproblems by setting (x + -121.5) equal to 101.524627554 and -101.524627554.Subproblem 1
x + -121.5 = 101.524627554 Simplifying x + -121.5 = 101.524627554 Reorder the terms: -121.5 + x = 101.524627554 Solving -121.5 + x = 101.524627554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '121.5' to each side of the equation. -121.5 + 121.5 + x = 101.524627554 + 121.5 Combine like terms: -121.5 + 121.5 = 0.0 0.0 + x = 101.524627554 + 121.5 x = 101.524627554 + 121.5 Combine like terms: 101.524627554 + 121.5 = 223.024627554 x = 223.024627554 Simplifying x = 223.024627554Subproblem 2
x + -121.5 = -101.524627554 Simplifying x + -121.5 = -101.524627554 Reorder the terms: -121.5 + x = -101.524627554 Solving -121.5 + x = -101.524627554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '121.5' to each side of the equation. -121.5 + 121.5 + x = -101.524627554 + 121.5 Combine like terms: -121.5 + 121.5 = 0.0 0.0 + x = -101.524627554 + 121.5 x = -101.524627554 + 121.5 Combine like terms: -101.524627554 + 121.5 = 19.975372446 x = 19.975372446 Simplifying x = 19.975372446Solution
The solution to the problem is based on the solutions from the subproblems. x = {223.024627554, 19.975372446}
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