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Simplifying x2 + 15x = -6 Reorder the terms: 15x + x2 = -6 Solving 15x + x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + 15x + x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 15x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 15x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 15x + x2 = 0 + -6 15x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 15x + x2 = -6 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 = -6 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -6 + 56.25 Combine like terms: -6 + 56.25 = 50.25 56.25 + 15x + x2 = 50.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + 7.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + 7.5 = 7.088723439 Simplifying x + 7.5 = 7.088723439 Reorder the terms: 7.5 + x = 7.088723439 Solving 7.5 + x = 7.088723439 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 = 7.088723439 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.088723439 + -7.5 x = 7.088723439 + -7.5 Combine like terms: 7.088723439 + -7.5 = -0.411276561 x = -0.411276561 Simplifying x = -0.411276561Subproblem 2
x + 7.5 = -7.088723439 Simplifying x + 7.5 = -7.088723439 Reorder the terms: 7.5 + x = -7.088723439 Solving 7.5 + x = -7.088723439 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 = -7.088723439 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.088723439 + -7.5 x = -7.088723439 + -7.5 Combine like terms: -7.088723439 + -7.5 = -14.588723439 x = -14.588723439 Simplifying x = -14.588723439Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.411276561, -14.588723439}
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