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Simplifying 6x2 + 13x + -2 = 0 Reorder the terms: -2 + 13x + 6x2 = 0 Solving -2 + 13x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.3333333333 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 2.166666667x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 2.166666667x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 2.166666667x + x2 = 0 + 0.3333333333 2.166666667x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 2.166666667x + x2 = 0.3333333333 The x term is 2.166666667x. Take half its coefficient (1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. 2.166666667x + 1.173611113 + x2 = 0.3333333333 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = 0.3333333333 + 1.173611113 Combine like terms: 0.3333333333 + 1.173611113 = 1.5069444463 1.173611113 + 2.166666667x + x2 = 1.5069444463 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = 1.5069444463 Calculate the square root of the right side: 1.227576656 Break this problem into two subproblems by setting (x + 1.083333334) equal to 1.227576656 and -1.227576656.Subproblem 1
x + 1.083333334 = 1.227576656 Simplifying x + 1.083333334 = 1.227576656 Reorder the terms: 1.083333334 + x = 1.227576656 Solving 1.083333334 + x = 1.227576656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = 1.227576656 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 1.227576656 + -1.083333334 x = 1.227576656 + -1.083333334 Combine like terms: 1.227576656 + -1.083333334 = 0.144243322 x = 0.144243322 Simplifying x = 0.144243322Subproblem 2
x + 1.083333334 = -1.227576656 Simplifying x + 1.083333334 = -1.227576656 Reorder the terms: 1.083333334 + x = -1.227576656 Solving 1.083333334 + x = -1.227576656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = -1.227576656 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -1.227576656 + -1.083333334 x = -1.227576656 + -1.083333334 Combine like terms: -1.227576656 + -1.083333334 = -2.31090999 x = -2.31090999 Simplifying x = -2.31090999Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.144243322, -2.31090999}
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