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Simplifying x2 + 15x + -10000 = 0 Reorder the terms: -10000 + 15x + x2 = 0 Solving -10000 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 15x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 15x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 15x + x2 = 0 + 10000 15x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 15x + x2 = 10000 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 = 10000 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 10000 + 56.25 Combine like terms: 10000 + 56.25 = 10056.25 56.25 + 15x + x2 = 10056.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 10056.25 Calculate the square root of the right side: 100.280855601 Break this problem into two subproblems by setting (x + 7.5) equal to 100.280855601 and -100.280855601.Subproblem 1
x + 7.5 = 100.280855601 Simplifying x + 7.5 = 100.280855601 Reorder the terms: 7.5 + x = 100.280855601 Solving 7.5 + x = 100.280855601 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 = 100.280855601 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 100.280855601 + -7.5 x = 100.280855601 + -7.5 Combine like terms: 100.280855601 + -7.5 = 92.780855601 x = 92.780855601 Simplifying x = 92.780855601Subproblem 2
x + 7.5 = -100.280855601 Simplifying x + 7.5 = -100.280855601 Reorder the terms: 7.5 + x = -100.280855601 Solving 7.5 + x = -100.280855601 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 = -100.280855601 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -100.280855601 + -7.5 x = -100.280855601 + -7.5 Combine like terms: -100.280855601 + -7.5 = -107.780855601 x = -107.780855601 Simplifying x = -107.780855601Solution
The solution to the problem is based on the solutions from the subproblems. x = {92.780855601, -107.780855601}
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