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Simplifying x = 4x2 + -24x + -72 Reorder the terms: x = -72 + -24x + 4x2 Solving x = -72 + -24x + 4x2 Solving for variable 'x'. Reorder the terms: 72 + x + 24x + -4x2 = -72 + -24x + 4x2 + 72 + 24x + -4x2 Combine like terms: x + 24x = 25x 72 + 25x + -4x2 = -72 + -24x + 4x2 + 72 + 24x + -4x2 Reorder the terms: 72 + 25x + -4x2 = -72 + 72 + -24x + 24x + 4x2 + -4x2 Combine like terms: -72 + 72 = 0 72 + 25x + -4x2 = 0 + -24x + 24x + 4x2 + -4x2 72 + 25x + -4x2 = -24x + 24x + 4x2 + -4x2 Combine like terms: -24x + 24x = 0 72 + 25x + -4x2 = 0 + 4x2 + -4x2 72 + 25x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 72 + 25x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -18 + -6.25x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -6.25x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -6.25x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -6.25x + x2 = 0 + 18 -6.25x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -6.25x + x2 = 18 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 18 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 18 + 9.765625 Combine like terms: 18 + 9.765625 = 27.765625 9.765625 + -6.25x + x2 = 27.765625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 27.765625 Calculate the square root of the right side: 5.269309727 Break this problem into two subproblems by setting (x + -3.125) equal to 5.269309727 and -5.269309727.Subproblem 1
x + -3.125 = 5.269309727 Simplifying x + -3.125 = 5.269309727 Reorder the terms: -3.125 + x = 5.269309727 Solving -3.125 + x = 5.269309727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 5.269309727 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 5.269309727 + 3.125 x = 5.269309727 + 3.125 Combine like terms: 5.269309727 + 3.125 = 8.394309727 x = 8.394309727 Simplifying x = 8.394309727Subproblem 2
x + -3.125 = -5.269309727 Simplifying x + -3.125 = -5.269309727 Reorder the terms: -3.125 + x = -5.269309727 Solving -3.125 + x = -5.269309727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -5.269309727 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -5.269309727 + 3.125 x = -5.269309727 + 3.125 Combine like terms: -5.269309727 + 3.125 = -2.144309727 x = -2.144309727 Simplifying x = -2.144309727Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.394309727, -2.144309727}
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