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Simplifying x2 + 15x + -98 = 0 Reorder the terms: -98 + 15x + x2 = 0 Solving -98 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + 15x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + 15x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + 15x + x2 = 0 + 98 15x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 15x + x2 = 98 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 = 98 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 98 + 56.25 Combine like terms: 98 + 56.25 = 154.25 56.25 + 15x + x2 = 154.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 154.25 Calculate the square root of the right side: 12.419742348 Break this problem into two subproblems by setting (x + 7.5) equal to 12.419742348 and -12.419742348.Subproblem 1
x + 7.5 = 12.419742348 Simplifying x + 7.5 = 12.419742348 Reorder the terms: 7.5 + x = 12.419742348 Solving 7.5 + x = 12.419742348 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 = 12.419742348 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 12.419742348 + -7.5 x = 12.419742348 + -7.5 Combine like terms: 12.419742348 + -7.5 = 4.919742348 x = 4.919742348 Simplifying x = 4.919742348Subproblem 2
x + 7.5 = -12.419742348 Simplifying x + 7.5 = -12.419742348 Reorder the terms: 7.5 + x = -12.419742348 Solving 7.5 + x = -12.419742348 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 = -12.419742348 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -12.419742348 + -7.5 x = -12.419742348 + -7.5 Combine like terms: -12.419742348 + -7.5 = -19.919742348 x = -19.919742348 Simplifying x = -19.919742348Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.919742348, -19.919742348}
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