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Simplifying x2 + 24x = -3x2 + 11 Reorder the terms: 24x + x2 = -3x2 + 11 Reorder the terms: 24x + x2 = 11 + -3x2 Solving 24x + x2 = 11 + -3x2 Solving for variable 'x'. Reorder the terms: -11 + 24x + x2 + 3x2 = 11 + -3x2 + -11 + 3x2 Combine like terms: x2 + 3x2 = 4x2 -11 + 24x + 4x2 = 11 + -3x2 + -11 + 3x2 Reorder the terms: -11 + 24x + 4x2 = 11 + -11 + -3x2 + 3x2 Combine like terms: 11 + -11 = 0 -11 + 24x + 4x2 = 0 + -3x2 + 3x2 -11 + 24x + 4x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -11 + 24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + 6x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 6x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 6x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 6x + x2 = 0 + 2.75 6x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 6x + x2 = 2.75 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 2.75 + 9 Reorder the terms: 9 + 6x + x2 = 2.75 + 9 Combine like terms: 2.75 + 9 = 11.75 9 + 6x + x2 = 11.75 Factor a perfect square on the left side: (x + 3)(x + 3) = 11.75 Calculate the square root of the right side: 3.4278273 Break this problem into two subproblems by setting (x + 3) equal to 3.4278273 and -3.4278273.Subproblem 1
x + 3 = 3.4278273 Simplifying x + 3 = 3.4278273 Reorder the terms: 3 + x = 3.4278273 Solving 3 + x = 3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.4278273 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.4278273 + -3 x = 3.4278273 + -3 Combine like terms: 3.4278273 + -3 = 0.4278273 x = 0.4278273 Simplifying x = 0.4278273Subproblem 2
x + 3 = -3.4278273 Simplifying x + 3 = -3.4278273 Reorder the terms: 3 + x = -3.4278273 Solving 3 + x = -3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.4278273 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.4278273 + -3 x = -3.4278273 + -3 Combine like terms: -3.4278273 + -3 = -6.4278273 x = -6.4278273 Simplifying x = -6.4278273Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4278273, -6.4278273}
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