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Simplifying x2 + 15x + -8400 = 0 Reorder the terms: -8400 + 15x + x2 = 0 Solving -8400 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8400' to each side of the equation. -8400 + 15x + 8400 + x2 = 0 + 8400 Reorder the terms: -8400 + 8400 + 15x + x2 = 0 + 8400 Combine like terms: -8400 + 8400 = 0 0 + 15x + x2 = 0 + 8400 15x + x2 = 0 + 8400 Combine like terms: 0 + 8400 = 8400 15x + x2 = 8400 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 = 8400 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 8400 + 56.25 Combine like terms: 8400 + 56.25 = 8456.25 56.25 + 15x + x2 = 8456.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 8456.25 Calculate the square root of the right side: 91.957870789 Break this problem into two subproblems by setting (x + 7.5) equal to 91.957870789 and -91.957870789.Subproblem 1
x + 7.5 = 91.957870789 Simplifying x + 7.5 = 91.957870789 Reorder the terms: 7.5 + x = 91.957870789 Solving 7.5 + x = 91.957870789 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 = 91.957870789 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 91.957870789 + -7.5 x = 91.957870789 + -7.5 Combine like terms: 91.957870789 + -7.5 = 84.457870789 x = 84.457870789 Simplifying x = 84.457870789Subproblem 2
x + 7.5 = -91.957870789 Simplifying x + 7.5 = -91.957870789 Reorder the terms: 7.5 + x = -91.957870789 Solving 7.5 + x = -91.957870789 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 = -91.957870789 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -91.957870789 + -7.5 x = -91.957870789 + -7.5 Combine like terms: -91.957870789 + -7.5 = -99.457870789 x = -99.457870789 Simplifying x = -99.457870789Solution
The solution to the problem is based on the solutions from the subproblems. x = {84.457870789, -99.457870789}
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