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Simplifying 6x2 + 25x + -168 = 0 Reorder the terms: -168 + 25x + 6x2 = 0 Solving -168 + 25x + 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'. -28 + 4.166666667x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 4.166666667x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 4.166666667x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 4.166666667x + x2 = 0 + 28 4.166666667x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 4.166666667x + x2 = 28 The x term is 4.166666667x. Take half its coefficient (2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. 4.166666667x + 4.340277781 + x2 = 28 + 4.340277781 Reorder the terms: 4.340277781 + 4.166666667x + x2 = 28 + 4.340277781 Combine like terms: 28 + 4.340277781 = 32.340277781 4.340277781 + 4.166666667x + x2 = 32.340277781 Factor a perfect square on the left side: (x + 2.083333334)(x + 2.083333334) = 32.340277781 Calculate the square root of the right side: 5.686851306 Break this problem into two subproblems by setting (x + 2.083333334) equal to 5.686851306 and -5.686851306.Subproblem 1
x + 2.083333334 = 5.686851306 Simplifying x + 2.083333334 = 5.686851306 Reorder the terms: 2.083333334 + x = 5.686851306 Solving 2.083333334 + x = 5.686851306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + x = 5.686851306 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = 5.686851306 + -2.083333334 x = 5.686851306 + -2.083333334 Combine like terms: 5.686851306 + -2.083333334 = 3.603517972 x = 3.603517972 Simplifying x = 3.603517972Subproblem 2
x + 2.083333334 = -5.686851306 Simplifying x + 2.083333334 = -5.686851306 Reorder the terms: 2.083333334 + x = -5.686851306 Solving 2.083333334 + x = -5.686851306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + x = -5.686851306 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = -5.686851306 + -2.083333334 x = -5.686851306 + -2.083333334 Combine like terms: -5.686851306 + -2.083333334 = -7.77018464 x = -7.77018464 Simplifying x = -7.77018464Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.603517972, -7.77018464}
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