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Simplifying x2 + 15x = 78 Reorder the terms: 15x + x2 = 78 Solving 15x + x2 = 78 Solving for variable 'x'. Reorder the terms: -78 + 15x + x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -78 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + 15x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + 15x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + 15x + x2 = 0 + 78 15x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 15x + x2 = 78 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 = 78 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 78 + 56.25 Combine like terms: 78 + 56.25 = 134.25 56.25 + 15x + x2 = 134.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 134.25 Calculate the square root of the right side: 11.586630226 Break this problem into two subproblems by setting (x + 7.5) equal to 11.586630226 and -11.586630226.Subproblem 1
x + 7.5 = 11.586630226 Simplifying x + 7.5 = 11.586630226 Reorder the terms: 7.5 + x = 11.586630226 Solving 7.5 + x = 11.586630226 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 = 11.586630226 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 11.586630226 + -7.5 x = 11.586630226 + -7.5 Combine like terms: 11.586630226 + -7.5 = 4.086630226 x = 4.086630226 Simplifying x = 4.086630226Subproblem 2
x + 7.5 = -11.586630226 Simplifying x + 7.5 = -11.586630226 Reorder the terms: 7.5 + x = -11.586630226 Solving 7.5 + x = -11.586630226 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 = -11.586630226 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -11.586630226 + -7.5 x = -11.586630226 + -7.5 Combine like terms: -11.586630226 + -7.5 = -19.086630226 x = -19.086630226 Simplifying x = -19.086630226Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.086630226, -19.086630226}
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