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Simplifying x2 + 15x + -54 = -3 Reorder the terms: -54 + 15x + x2 = -3 Solving -54 + 15x + x2 = -3 Solving for variable 'x'. Reorder the terms: -54 + 3 + 15x + x2 = -3 + 3 Combine like terms: -54 + 3 = -51 -51 + 15x + x2 = -3 + 3 Combine like terms: -3 + 3 = 0 -51 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 15x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + 15x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 15x + x2 = 0 + 51 15x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 15x + x2 = 51 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 51 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 51 + 56.25 Combine like terms: 51 + 56.25 = 107.25 56.25 + 15x + x2 = 107.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 107.25 Calculate the square root of the right side: 10.356157589 Break this problem into two subproblems by setting (x + 7.5) equal to 10.356157589 and -10.356157589.Subproblem 1
x + 7.5 = 10.356157589 Simplifying x + 7.5 = 10.356157589 Reorder the terms: 7.5 + x = 10.356157589 Solving 7.5 + x = 10.356157589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 10.356157589 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 10.356157589 + -7.5 x = 10.356157589 + -7.5 Combine like terms: 10.356157589 + -7.5 = 2.856157589 x = 2.856157589 Simplifying x = 2.856157589Subproblem 2
x + 7.5 = -10.356157589 Simplifying x + 7.5 = -10.356157589 Reorder the terms: 7.5 + x = -10.356157589 Solving 7.5 + x = -10.356157589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -10.356157589 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -10.356157589 + -7.5 x = -10.356157589 + -7.5 Combine like terms: -10.356157589 + -7.5 = -17.856157589 x = -17.856157589 Simplifying x = -17.856157589Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.856157589, -17.856157589}
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