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Simplifying 4x2 = 24x + -5 Reorder the terms: 4x2 = -5 + 24x Solving 4x2 = -5 + 24x Solving for variable 'x'. Reorder the terms: 5 + -24x + 4x2 = -5 + 24x + 5 + -24x Reorder the terms: 5 + -24x + 4x2 = -5 + 5 + 24x + -24x Combine like terms: -5 + 5 = 0 5 + -24x + 4x2 = 0 + 24x + -24x 5 + -24x + 4x2 = 24x + -24x Combine like terms: 24x + -24x = 0 5 + -24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -6x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -6x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -6x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -6x + x2 = 0 + -1.25 -6x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -6x + x2 = -1.25 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 = -1.25 + 9 Reorder the terms: 9 + -6x + x2 = -1.25 + 9 Combine like terms: -1.25 + 9 = 7.75 9 + -6x + x2 = 7.75 Factor a perfect square on the left side: (x + -3)(x + -3) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (x + -3) equal to 2.783882181 and -2.783882181.Subproblem 1
x + -3 = 2.783882181 Simplifying x + -3 = 2.783882181 Reorder the terms: -3 + x = 2.783882181 Solving -3 + x = 2.783882181 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 = 2.783882181 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.783882181 + 3 x = 2.783882181 + 3 Combine like terms: 2.783882181 + 3 = 5.783882181 x = 5.783882181 Simplifying x = 5.783882181Subproblem 2
x + -3 = -2.783882181 Simplifying x + -3 = -2.783882181 Reorder the terms: -3 + x = -2.783882181 Solving -3 + x = -2.783882181 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 = -2.783882181 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.783882181 + 3 x = -2.783882181 + 3 Combine like terms: -2.783882181 + 3 = 0.216117819 x = 0.216117819 Simplifying x = 0.216117819Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.783882181, 0.216117819}
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