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Simplifying 4x2 + -24x = -1 Reorder the terms: -24x + 4x2 = -1 Solving -24x + 4x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + -24x + 4x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -6x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -6x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -6x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -6x + x2 = 0 + -0.25 -6x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -6x + x2 = -0.25 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 = -0.25 + 9 Reorder the terms: 9 + -6x + x2 = -0.25 + 9 Combine like terms: -0.25 + 9 = 8.75 9 + -6x + x2 = 8.75 Factor a perfect square on the left side: (x + -3)(x + -3) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (x + -3) equal to 2.958039892 and -2.958039892.Subproblem 1
x + -3 = 2.958039892 Simplifying x + -3 = 2.958039892 Reorder the terms: -3 + x = 2.958039892 Solving -3 + x = 2.958039892 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 = 2.958039892 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.958039892 + 3 x = 2.958039892 + 3 Combine like terms: 2.958039892 + 3 = 5.958039892 x = 5.958039892 Simplifying x = 5.958039892Subproblem 2
x + -3 = -2.958039892 Simplifying x + -3 = -2.958039892 Reorder the terms: -3 + x = -2.958039892 Solving -3 + x = -2.958039892 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 = -2.958039892 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.958039892 + 3 x = -2.958039892 + 3 Combine like terms: -2.958039892 + 3 = 0.041960108 x = 0.041960108 Simplifying x = 0.041960108Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.958039892, 0.041960108}
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