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Simplifying 25x2 + -119x + -94 = 0 Reorder the terms: -94 + -119x + 25x2 = 0 Solving -94 + -119x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -3.76 + -4.76x + x2 = 0 Move the constant term to the right: Add '3.76' to each side of the equation. -3.76 + -4.76x + 3.76 + x2 = 0 + 3.76 Reorder the terms: -3.76 + 3.76 + -4.76x + x2 = 0 + 3.76 Combine like terms: -3.76 + 3.76 = 0.00 0.00 + -4.76x + x2 = 0 + 3.76 -4.76x + x2 = 0 + 3.76 Combine like terms: 0 + 3.76 = 3.76 -4.76x + x2 = 3.76 The x term is -4.76x. Take half its coefficient (-2.38). Square it (5.6644) and add it to both sides. Add '5.6644' to each side of the equation. -4.76x + 5.6644 + x2 = 3.76 + 5.6644 Reorder the terms: 5.6644 + -4.76x + x2 = 3.76 + 5.6644 Combine like terms: 3.76 + 5.6644 = 9.4244 5.6644 + -4.76x + x2 = 9.4244 Factor a perfect square on the left side: (x + -2.38)(x + -2.38) = 9.4244 Calculate the square root of the right side: 3.069918566 Break this problem into two subproblems by setting (x + -2.38) equal to 3.069918566 and -3.069918566.Subproblem 1
x + -2.38 = 3.069918566 Simplifying x + -2.38 = 3.069918566 Reorder the terms: -2.38 + x = 3.069918566 Solving -2.38 + x = 3.069918566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.38' to each side of the equation. -2.38 + 2.38 + x = 3.069918566 + 2.38 Combine like terms: -2.38 + 2.38 = 0.00 0.00 + x = 3.069918566 + 2.38 x = 3.069918566 + 2.38 Combine like terms: 3.069918566 + 2.38 = 5.449918566 x = 5.449918566 Simplifying x = 5.449918566Subproblem 2
x + -2.38 = -3.069918566 Simplifying x + -2.38 = -3.069918566 Reorder the terms: -2.38 + x = -3.069918566 Solving -2.38 + x = -3.069918566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.38' to each side of the equation. -2.38 + 2.38 + x = -3.069918566 + 2.38 Combine like terms: -2.38 + 2.38 = 0.00 0.00 + x = -3.069918566 + 2.38 x = -3.069918566 + 2.38 Combine like terms: -3.069918566 + 2.38 = -0.689918566 x = -0.689918566 Simplifying x = -0.689918566Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.449918566, -0.689918566}
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