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Simplifying 2.12x2 + -3.25x + -10 = 0 Reorder the terms: -10 + -3.25x + 2.12x2 = 0 Solving -10 + -3.25x + 2.12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.12 the coefficient of the squared term: Divide each side by '2.12'. -4.716981132 + -1.533018868x + x2 = 0 Move the constant term to the right: Add '4.716981132' to each side of the equation. -4.716981132 + -1.533018868x + 4.716981132 + x2 = 0 + 4.716981132 Reorder the terms: -4.716981132 + 4.716981132 + -1.533018868x + x2 = 0 + 4.716981132 Combine like terms: -4.716981132 + 4.716981132 = 0.000000000 0.000000000 + -1.533018868x + x2 = 0 + 4.716981132 -1.533018868x + x2 = 0 + 4.716981132 Combine like terms: 0 + 4.716981132 = 4.716981132 -1.533018868x + x2 = 4.716981132 The x term is -1.533018868x. Take half its coefficient (-0.766509434). Square it (0.5875367124) and add it to both sides. Add '0.5875367124' to each side of the equation. -1.533018868x + 0.5875367124 + x2 = 4.716981132 + 0.5875367124 Reorder the terms: 0.5875367124 + -1.533018868x + x2 = 4.716981132 + 0.5875367124 Combine like terms: 4.716981132 + 0.5875367124 = 5.3045178444 0.5875367124 + -1.533018868x + x2 = 5.3045178444 Factor a perfect square on the left side: (x + -0.766509434)(x + -0.766509434) = 5.3045178444 Calculate the square root of the right side: 2.303153891 Break this problem into two subproblems by setting (x + -0.766509434) equal to 2.303153891 and -2.303153891.Subproblem 1
x + -0.766509434 = 2.303153891 Simplifying x + -0.766509434 = 2.303153891 Reorder the terms: -0.766509434 + x = 2.303153891 Solving -0.766509434 + x = 2.303153891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.766509434' to each side of the equation. -0.766509434 + 0.766509434 + x = 2.303153891 + 0.766509434 Combine like terms: -0.766509434 + 0.766509434 = 0.000000000 0.000000000 + x = 2.303153891 + 0.766509434 x = 2.303153891 + 0.766509434 Combine like terms: 2.303153891 + 0.766509434 = 3.069663325 x = 3.069663325 Simplifying x = 3.069663325Subproblem 2
x + -0.766509434 = -2.303153891 Simplifying x + -0.766509434 = -2.303153891 Reorder the terms: -0.766509434 + x = -2.303153891 Solving -0.766509434 + x = -2.303153891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.766509434' to each side of the equation. -0.766509434 + 0.766509434 + x = -2.303153891 + 0.766509434 Combine like terms: -0.766509434 + 0.766509434 = 0.000000000 0.000000000 + x = -2.303153891 + 0.766509434 x = -2.303153891 + 0.766509434 Combine like terms: -2.303153891 + 0.766509434 = -1.536644457 x = -1.536644457 Simplifying x = -1.536644457Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.069663325, -1.536644457}
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