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Simplifying 0 = -6x2 + 24x + -5 Reorder the terms: 0 = -5 + 24x + -6x2 Solving 0 = -5 + 24x + -6x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + -24x + 6x2 = -5 + 24x + -6x2 + 5 + -24x + 6x2 Reorder the terms: 5 + -24x + 6x2 = -5 + 5 + 24x + -24x + -6x2 + 6x2 Combine like terms: -5 + 5 = 0 5 + -24x + 6x2 = 0 + 24x + -24x + -6x2 + 6x2 5 + -24x + 6x2 = 24x + -24x + -6x2 + 6x2 Combine like terms: 24x + -24x = 0 5 + -24x + 6x2 = 0 + -6x2 + 6x2 5 + -24x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 5 + -24x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + -4x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -4x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -4x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + -0.8333333333 -4x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -4x + x2 = -0.8333333333 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -0.8333333333 + 4 Reorder the terms: 4 + -4x + x2 = -0.8333333333 + 4 Combine like terms: -0.8333333333 + 4 = 3.1666666667 4 + -4x + x2 = 3.1666666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.1666666667 Calculate the square root of the right side: 1.779513042 Break this problem into two subproblems by setting (x + -2) equal to 1.779513042 and -1.779513042.Subproblem 1
x + -2 = 1.779513042 Simplifying x + -2 = 1.779513042 Reorder the terms: -2 + x = 1.779513042 Solving -2 + x = 1.779513042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.779513042 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.779513042 + 2 x = 1.779513042 + 2 Combine like terms: 1.779513042 + 2 = 3.779513042 x = 3.779513042 Simplifying x = 3.779513042Subproblem 2
x + -2 = -1.779513042 Simplifying x + -2 = -1.779513042 Reorder the terms: -2 + x = -1.779513042 Solving -2 + x = -1.779513042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.779513042 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.779513042 + 2 x = -1.779513042 + 2 Combine like terms: -1.779513042 + 2 = 0.220486958 x = 0.220486958 Simplifying x = 0.220486958Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.779513042, 0.220486958}
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