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Simplifying x2 + 15x = 49 Reorder the terms: 15x + x2 = 49 Solving 15x + x2 = 49 Solving for variable 'x'. Reorder the terms: -49 + 15x + x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 15x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 15x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 15x + x2 = 0 + 49 15x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 15x + x2 = 49 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 = 49 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 49 + 56.25 Combine like terms: 49 + 56.25 = 105.25 56.25 + 15x + x2 = 105.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 105.25 Calculate the square root of the right side: 10.259142264 Break this problem into two subproblems by setting (x + 7.5) equal to 10.259142264 and -10.259142264.Subproblem 1
x + 7.5 = 10.259142264 Simplifying x + 7.5 = 10.259142264 Reorder the terms: 7.5 + x = 10.259142264 Solving 7.5 + x = 10.259142264 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 = 10.259142264 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 10.259142264 + -7.5 x = 10.259142264 + -7.5 Combine like terms: 10.259142264 + -7.5 = 2.759142264 x = 2.759142264 Simplifying x = 2.759142264Subproblem 2
x + 7.5 = -10.259142264 Simplifying x + 7.5 = -10.259142264 Reorder the terms: 7.5 + x = -10.259142264 Solving 7.5 + x = -10.259142264 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 = -10.259142264 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -10.259142264 + -7.5 x = -10.259142264 + -7.5 Combine like terms: -10.259142264 + -7.5 = -17.759142264 x = -17.759142264 Simplifying x = -17.759142264Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.759142264, -17.759142264}
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