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Simplifying 25x2 + -146x + -39 = 0 Reorder the terms: -39 + -146x + 25x2 = 0 Solving -39 + -146x + 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'. -1.56 + -5.84x + x2 = 0 Move the constant term to the right: Add '1.56' to each side of the equation. -1.56 + -5.84x + 1.56 + x2 = 0 + 1.56 Reorder the terms: -1.56 + 1.56 + -5.84x + x2 = 0 + 1.56 Combine like terms: -1.56 + 1.56 = 0.00 0.00 + -5.84x + x2 = 0 + 1.56 -5.84x + x2 = 0 + 1.56 Combine like terms: 0 + 1.56 = 1.56 -5.84x + x2 = 1.56 The x term is -5.84x. Take half its coefficient (-2.92). Square it (8.5264) and add it to both sides. Add '8.5264' to each side of the equation. -5.84x + 8.5264 + x2 = 1.56 + 8.5264 Reorder the terms: 8.5264 + -5.84x + x2 = 1.56 + 8.5264 Combine like terms: 1.56 + 8.5264 = 10.0864 8.5264 + -5.84x + x2 = 10.0864 Factor a perfect square on the left side: (x + -2.92)(x + -2.92) = 10.0864 Calculate the square root of the right side: 3.175909319 Break this problem into two subproblems by setting (x + -2.92) equal to 3.175909319 and -3.175909319.Subproblem 1
x + -2.92 = 3.175909319 Simplifying x + -2.92 = 3.175909319 Reorder the terms: -2.92 + x = 3.175909319 Solving -2.92 + x = 3.175909319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.92' to each side of the equation. -2.92 + 2.92 + x = 3.175909319 + 2.92 Combine like terms: -2.92 + 2.92 = 0.00 0.00 + x = 3.175909319 + 2.92 x = 3.175909319 + 2.92 Combine like terms: 3.175909319 + 2.92 = 6.095909319 x = 6.095909319 Simplifying x = 6.095909319Subproblem 2
x + -2.92 = -3.175909319 Simplifying x + -2.92 = -3.175909319 Reorder the terms: -2.92 + x = -3.175909319 Solving -2.92 + x = -3.175909319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.92' to each side of the equation. -2.92 + 2.92 + x = -3.175909319 + 2.92 Combine like terms: -2.92 + 2.92 = 0.00 0.00 + x = -3.175909319 + 2.92 x = -3.175909319 + 2.92 Combine like terms: -3.175909319 + 2.92 = -0.255909319 x = -0.255909319 Simplifying x = -0.255909319Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.095909319, -0.255909319}
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