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Simplifying x2 + 15x = 360 Reorder the terms: 15x + x2 = 360 Solving 15x + x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 15x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 15x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 15x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 15x + x2 = 0 + 360 15x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 15x + x2 = 360 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 = 360 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 360 + 56.25 Combine like terms: 360 + 56.25 = 416.25 56.25 + 15x + x2 = 416.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 416.25 Calculate the square root of the right side: 20.402205763 Break this problem into two subproblems by setting (x + 7.5) equal to 20.402205763 and -20.402205763.Subproblem 1
x + 7.5 = 20.402205763 Simplifying x + 7.5 = 20.402205763 Reorder the terms: 7.5 + x = 20.402205763 Solving 7.5 + x = 20.402205763 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 = 20.402205763 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 20.402205763 + -7.5 x = 20.402205763 + -7.5 Combine like terms: 20.402205763 + -7.5 = 12.902205763 x = 12.902205763 Simplifying x = 12.902205763Subproblem 2
x + 7.5 = -20.402205763 Simplifying x + 7.5 = -20.402205763 Reorder the terms: 7.5 + x = -20.402205763 Solving 7.5 + x = -20.402205763 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 = -20.402205763 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -20.402205763 + -7.5 x = -20.402205763 + -7.5 Combine like terms: -20.402205763 + -7.5 = -27.902205763 x = -27.902205763 Simplifying x = -27.902205763Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.902205763, -27.902205763}
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