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Simplifying 2178x2 + 5286x + -89875 = 0 Reorder the terms: -89875 + 5286x + 2178x2 = 0 Solving -89875 + 5286x + 2178x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2178 the coefficient of the squared term: Divide each side by '2178'. -41.26492195 + 2.426997245x + x2 = 0 Move the constant term to the right: Add '41.26492195' to each side of the equation. -41.26492195 + 2.426997245x + 41.26492195 + x2 = 0 + 41.26492195 Reorder the terms: -41.26492195 + 41.26492195 + 2.426997245x + x2 = 0 + 41.26492195 Combine like terms: -41.26492195 + 41.26492195 = 0.00000000 0.00000000 + 2.426997245x + x2 = 0 + 41.26492195 2.426997245x + x2 = 0 + 41.26492195 Combine like terms: 0 + 41.26492195 = 41.26492195 2.426997245x + x2 = 41.26492195 The x term is 2.426997245x. Take half its coefficient (1.213498623). Square it (1.472578908) and add it to both sides. Add '1.472578908' to each side of the equation. 2.426997245x + 1.472578908 + x2 = 41.26492195 + 1.472578908 Reorder the terms: 1.472578908 + 2.426997245x + x2 = 41.26492195 + 1.472578908 Combine like terms: 41.26492195 + 1.472578908 = 42.737500858 1.472578908 + 2.426997245x + x2 = 42.737500858 Factor a perfect square on the left side: (x + 1.213498623)(x + 1.213498623) = 42.737500858 Calculate the square root of the right side: 6.537392512 Break this problem into two subproblems by setting (x + 1.213498623) equal to 6.537392512 and -6.537392512.Subproblem 1
x + 1.213498623 = 6.537392512 Simplifying x + 1.213498623 = 6.537392512 Reorder the terms: 1.213498623 + x = 6.537392512 Solving 1.213498623 + x = 6.537392512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.213498623' to each side of the equation. 1.213498623 + -1.213498623 + x = 6.537392512 + -1.213498623 Combine like terms: 1.213498623 + -1.213498623 = 0.000000000 0.000000000 + x = 6.537392512 + -1.213498623 x = 6.537392512 + -1.213498623 Combine like terms: 6.537392512 + -1.213498623 = 5.323893889 x = 5.323893889 Simplifying x = 5.323893889Subproblem 2
x + 1.213498623 = -6.537392512 Simplifying x + 1.213498623 = -6.537392512 Reorder the terms: 1.213498623 + x = -6.537392512 Solving 1.213498623 + x = -6.537392512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.213498623' to each side of the equation. 1.213498623 + -1.213498623 + x = -6.537392512 + -1.213498623 Combine like terms: 1.213498623 + -1.213498623 = 0.000000000 0.000000000 + x = -6.537392512 + -1.213498623 x = -6.537392512 + -1.213498623 Combine like terms: -6.537392512 + -1.213498623 = -7.750891135 x = -7.750891135 Simplifying x = -7.750891135Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.323893889, -7.750891135}
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