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Simplifying 0 = -1x2 + 798x + -6900 Reorder the terms: 0 = -6900 + 798x + -1x2 Solving 0 = -6900 + 798x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 6900 = 6900 6900 + -798x + x2 = -6900 + 798x + -1x2 + 6900 + -798x + x2 Reorder the terms: 6900 + -798x + x2 = -6900 + 6900 + 798x + -798x + -1x2 + x2 Combine like terms: -6900 + 6900 = 0 6900 + -798x + x2 = 0 + 798x + -798x + -1x2 + x2 6900 + -798x + x2 = 798x + -798x + -1x2 + x2 Combine like terms: 798x + -798x = 0 6900 + -798x + x2 = 0 + -1x2 + x2 6900 + -798x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 6900 + -798x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6900' to each side of the equation. 6900 + -798x + -6900 + x2 = 0 + -6900 Reorder the terms: 6900 + -6900 + -798x + x2 = 0 + -6900 Combine like terms: 6900 + -6900 = 0 0 + -798x + x2 = 0 + -6900 -798x + x2 = 0 + -6900 Combine like terms: 0 + -6900 = -6900 -798x + x2 = -6900 The x term is -798x. Take half its coefficient (-399). Square it (159201) and add it to both sides. Add '159201' to each side of the equation. -798x + 159201 + x2 = -6900 + 159201 Reorder the terms: 159201 + -798x + x2 = -6900 + 159201 Combine like terms: -6900 + 159201 = 152301 159201 + -798x + x2 = 152301 Factor a perfect square on the left side: (x + -399)(x + -399) = 152301 Calculate the square root of the right side: 390.257607229 Break this problem into two subproblems by setting (x + -399) equal to 390.257607229 and -390.257607229.Subproblem 1
x + -399 = 390.257607229 Simplifying x + -399 = 390.257607229 Reorder the terms: -399 + x = 390.257607229 Solving -399 + x = 390.257607229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '399' to each side of the equation. -399 + 399 + x = 390.257607229 + 399 Combine like terms: -399 + 399 = 0 0 + x = 390.257607229 + 399 x = 390.257607229 + 399 Combine like terms: 390.257607229 + 399 = 789.257607229 x = 789.257607229 Simplifying x = 789.257607229Subproblem 2
x + -399 = -390.257607229 Simplifying x + -399 = -390.257607229 Reorder the terms: -399 + x = -390.257607229 Solving -399 + x = -390.257607229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '399' to each side of the equation. -399 + 399 + x = -390.257607229 + 399 Combine like terms: -399 + 399 = 0 0 + x = -390.257607229 + 399 x = -390.257607229 + 399 Combine like terms: -390.257607229 + 399 = 8.742392771 x = 8.742392771 Simplifying x = 8.742392771Solution
The solution to the problem is based on the solutions from the subproblems. x = {789.257607229, 8.742392771}
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