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Simplifying x2 + 15x + -300 = 0 Reorder the terms: -300 + 15x + x2 = 0 Solving -300 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 15x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 15x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 15x + x2 = 0 + 300 15x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 15x + x2 = 300 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 = 300 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 300 + 56.25 Combine like terms: 300 + 56.25 = 356.25 56.25 + 15x + x2 = 356.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 356.25 Calculate the square root of the right side: 18.874586088 Break this problem into two subproblems by setting (x + 7.5) equal to 18.874586088 and -18.874586088.Subproblem 1
x + 7.5 = 18.874586088 Simplifying x + 7.5 = 18.874586088 Reorder the terms: 7.5 + x = 18.874586088 Solving 7.5 + x = 18.874586088 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 = 18.874586088 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 18.874586088 + -7.5 x = 18.874586088 + -7.5 Combine like terms: 18.874586088 + -7.5 = 11.374586088 x = 11.374586088 Simplifying x = 11.374586088Subproblem 2
x + 7.5 = -18.874586088 Simplifying x + 7.5 = -18.874586088 Reorder the terms: 7.5 + x = -18.874586088 Solving 7.5 + x = -18.874586088 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 = -18.874586088 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -18.874586088 + -7.5 x = -18.874586088 + -7.5 Combine like terms: -18.874586088 + -7.5 = -26.374586088 x = -26.374586088 Simplifying x = -26.374586088Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.374586088, -26.374586088}
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