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Simplifying x2 + 3x + -54 = 55 Reorder the terms: -54 + 3x + x2 = 55 Solving -54 + 3x + x2 = 55 Solving for variable 'x'. Reorder the terms: -54 + -55 + 3x + x2 = 55 + -55 Combine like terms: -54 + -55 = -109 -109 + 3x + x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -109 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '109' to each side of the equation. -109 + 3x + 109 + x2 = 0 + 109 Reorder the terms: -109 + 109 + 3x + x2 = 0 + 109 Combine like terms: -109 + 109 = 0 0 + 3x + x2 = 0 + 109 3x + x2 = 0 + 109 Combine like terms: 0 + 109 = 109 3x + x2 = 109 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 109 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 109 + 2.25 Combine like terms: 109 + 2.25 = 111.25 2.25 + 3x + x2 = 111.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 111.25 Calculate the square root of the right side: 10.547511555 Break this problem into two subproblems by setting (x + 1.5) equal to 10.547511555 and -10.547511555.Subproblem 1
x + 1.5 = 10.547511555 Simplifying x + 1.5 = 10.547511555 Reorder the terms: 1.5 + x = 10.547511555 Solving 1.5 + x = 10.547511555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 10.547511555 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.547511555 + -1.5 x = 10.547511555 + -1.5 Combine like terms: 10.547511555 + -1.5 = 9.047511555 x = 9.047511555 Simplifying x = 9.047511555Subproblem 2
x + 1.5 = -10.547511555 Simplifying x + 1.5 = -10.547511555 Reorder the terms: 1.5 + x = -10.547511555 Solving 1.5 + x = -10.547511555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -10.547511555 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.547511555 + -1.5 x = -10.547511555 + -1.5 Combine like terms: -10.547511555 + -1.5 = -12.047511555 x = -12.047511555 Simplifying x = -12.047511555Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.047511555, -12.047511555}
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