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Simplifying 0 = x2 + 29x + -54 Reorder the terms: 0 = -54 + 29x + x2 Solving 0 = -54 + 29x + x2 Solving for variable 'x'. Combine like terms: 0 + 54 = 54 54 + -29x + -1x2 = -54 + 29x + x2 + 54 + -29x + -1x2 Reorder the terms: 54 + -29x + -1x2 = -54 + 54 + 29x + -29x + x2 + -1x2 Combine like terms: -54 + 54 = 0 54 + -29x + -1x2 = 0 + 29x + -29x + x2 + -1x2 54 + -29x + -1x2 = 29x + -29x + x2 + -1x2 Combine like terms: 29x + -29x = 0 54 + -29x + -1x2 = 0 + x2 + -1x2 54 + -29x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 54 + -29x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -54 + 29x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + 29x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 29x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 29x + x2 = 0 + 54 29x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 29x + x2 = 54 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = 54 + 210.25 Reorder the terms: 210.25 + 29x + x2 = 54 + 210.25 Combine like terms: 54 + 210.25 = 264.25 210.25 + 29x + x2 = 264.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 264.25 Calculate the square root of the right side: 16.255768207 Break this problem into two subproblems by setting (x + 14.5) equal to 16.255768207 and -16.255768207.Subproblem 1
x + 14.5 = 16.255768207 Simplifying x + 14.5 = 16.255768207 Reorder the terms: 14.5 + x = 16.255768207 Solving 14.5 + x = 16.255768207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 16.255768207 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 16.255768207 + -14.5 x = 16.255768207 + -14.5 Combine like terms: 16.255768207 + -14.5 = 1.755768207 x = 1.755768207 Simplifying x = 1.755768207Subproblem 2
x + 14.5 = -16.255768207 Simplifying x + 14.5 = -16.255768207 Reorder the terms: 14.5 + x = -16.255768207 Solving 14.5 + x = -16.255768207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -16.255768207 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -16.255768207 + -14.5 x = -16.255768207 + -14.5 Combine like terms: -16.255768207 + -14.5 = -30.755768207 x = -30.755768207 Simplifying x = -30.755768207Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.755768207, -30.755768207}
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