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Simplifying 4x2 + 24x + -23.6 = 0 Reorder the terms: -23.6 + 24x + 4x2 = 0 Solving -23.6 + 24x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.9 + 6x + x2 = 0 Move the constant term to the right: Add '5.9' to each side of the equation. -5.9 + 6x + 5.9 + x2 = 0 + 5.9 Reorder the terms: -5.9 + 5.9 + 6x + x2 = 0 + 5.9 Combine like terms: -5.9 + 5.9 = 0.0 0.0 + 6x + x2 = 0 + 5.9 6x + x2 = 0 + 5.9 Combine like terms: 0 + 5.9 = 5.9 6x + x2 = 5.9 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 = 5.9 + 9 Reorder the terms: 9 + 6x + x2 = 5.9 + 9 Combine like terms: 5.9 + 9 = 14.9 9 + 6x + x2 = 14.9 Factor a perfect square on the left side: (x + 3)(x + 3) = 14.9 Calculate the square root of the right side: 3.860051813 Break this problem into two subproblems by setting (x + 3) equal to 3.860051813 and -3.860051813.Subproblem 1
x + 3 = 3.860051813 Simplifying x + 3 = 3.860051813 Reorder the terms: 3 + x = 3.860051813 Solving 3 + x = 3.860051813 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 = 3.860051813 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.860051813 + -3 x = 3.860051813 + -3 Combine like terms: 3.860051813 + -3 = 0.860051813 x = 0.860051813 Simplifying x = 0.860051813Subproblem 2
x + 3 = -3.860051813 Simplifying x + 3 = -3.860051813 Reorder the terms: 3 + x = -3.860051813 Solving 3 + x = -3.860051813 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 = -3.860051813 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.860051813 + -3 x = -3.860051813 + -3 Combine like terms: -3.860051813 + -3 = -6.860051813 x = -6.860051813 Simplifying x = -6.860051813Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.860051813, -6.860051813}
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