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Simplifying 0 = -3x2 + -24x + 11 Reorder the terms: 0 = 11 + -24x + -3x2 Solving 0 = 11 + -24x + -3x2 Solving for variable 'x'. Combine like terms: 0 + -11 = -11 -11 + 24x + 3x2 = 11 + -24x + -3x2 + -11 + 24x + 3x2 Reorder the terms: -11 + 24x + 3x2 = 11 + -11 + -24x + 24x + -3x2 + 3x2 Combine like terms: 11 + -11 = 0 -11 + 24x + 3x2 = 0 + -24x + 24x + -3x2 + 3x2 -11 + 24x + 3x2 = -24x + 24x + -3x2 + 3x2 Combine like terms: -24x + 24x = 0 -11 + 24x + 3x2 = 0 + -3x2 + 3x2 -11 + 24x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -11 + 24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.666666667 + 8x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 8x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 8x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 8x + x2 = 0 + 3.666666667 8x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 8x + x2 = 3.666666667 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 3.666666667 + 16 Reorder the terms: 16 + 8x + x2 = 3.666666667 + 16 Combine like terms: 3.666666667 + 16 = 19.666666667 16 + 8x + x2 = 19.666666667 Factor a perfect square on the left side: (x + 4)(x + 4) = 19.666666667 Calculate the square root of the right side: 4.434711565 Break this problem into two subproblems by setting (x + 4) equal to 4.434711565 and -4.434711565.Subproblem 1
x + 4 = 4.434711565 Simplifying x + 4 = 4.434711565 Reorder the terms: 4 + x = 4.434711565 Solving 4 + x = 4.434711565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.434711565 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.434711565 + -4 x = 4.434711565 + -4 Combine like terms: 4.434711565 + -4 = 0.434711565 x = 0.434711565 Simplifying x = 0.434711565Subproblem 2
x + 4 = -4.434711565 Simplifying x + 4 = -4.434711565 Reorder the terms: 4 + x = -4.434711565 Solving 4 + x = -4.434711565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.434711565 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.434711565 + -4 x = -4.434711565 + -4 Combine like terms: -4.434711565 + -4 = -8.434711565 x = -8.434711565 Simplifying x = -8.434711565Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.434711565, -8.434711565}
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