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Simplifying 6x2 + -25x + -24 = 0 Reorder the terms: -24 + -25x + 6x2 = 0 Solving -24 + -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'. -4 + -4.166666667x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4.166666667x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -4.166666667x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4.166666667x + x2 = 0 + 4 -4.166666667x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4.166666667x + x2 = 4 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 = 4 + 4.340277781 Reorder the terms: 4.340277781 + -4.166666667x + x2 = 4 + 4.340277781 Combine like terms: 4 + 4.340277781 = 8.340277781 4.340277781 + -4.166666667x + x2 = 8.340277781 Factor a perfect square on the left side: (x + -2.083333334)(x + -2.083333334) = 8.340277781 Calculate the square root of the right side: 2.887953909 Break this problem into two subproblems by setting (x + -2.083333334) equal to 2.887953909 and -2.887953909.Subproblem 1
x + -2.083333334 = 2.887953909 Simplifying x + -2.083333334 = 2.887953909 Reorder the terms: -2.083333334 + x = 2.887953909 Solving -2.083333334 + x = 2.887953909 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 = 2.887953909 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = 2.887953909 + 2.083333334 x = 2.887953909 + 2.083333334 Combine like terms: 2.887953909 + 2.083333334 = 4.971287243 x = 4.971287243 Simplifying x = 4.971287243Subproblem 2
x + -2.083333334 = -2.887953909 Simplifying x + -2.083333334 = -2.887953909 Reorder the terms: -2.083333334 + x = -2.887953909 Solving -2.083333334 + x = -2.887953909 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 = -2.887953909 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = -2.887953909 + 2.083333334 x = -2.887953909 + 2.083333334 Combine like terms: -2.887953909 + 2.083333334 = -0.804620575 x = -0.804620575 Simplifying x = -0.804620575Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.971287243, -0.804620575}
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