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Simplifying x2 + 15x + -45 = 0 Reorder the terms: -45 + 15x + x2 = 0 Solving -45 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 15x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 15x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 15x + x2 = 0 + 45 15x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 15x + x2 = 45 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 = 45 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 45 + 56.25 Combine like terms: 45 + 56.25 = 101.25 56.25 + 15x + x2 = 101.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 101.25 Calculate the square root of the right side: 10.062305899 Break this problem into two subproblems by setting (x + 7.5) equal to 10.062305899 and -10.062305899.Subproblem 1
x + 7.5 = 10.062305899 Simplifying x + 7.5 = 10.062305899 Reorder the terms: 7.5 + x = 10.062305899 Solving 7.5 + x = 10.062305899 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 = 10.062305899 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 10.062305899 + -7.5 x = 10.062305899 + -7.5 Combine like terms: 10.062305899 + -7.5 = 2.562305899 x = 2.562305899 Simplifying x = 2.562305899Subproblem 2
x + 7.5 = -10.062305899 Simplifying x + 7.5 = -10.062305899 Reorder the terms: 7.5 + x = -10.062305899 Solving 7.5 + x = -10.062305899 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 = -10.062305899 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -10.062305899 + -7.5 x = -10.062305899 + -7.5 Combine like terms: -10.062305899 + -7.5 = -17.562305899 x = -17.562305899 Simplifying x = -17.562305899Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.562305899, -17.562305899}
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