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Simplifying 2x2 + -24x = -36 Reorder the terms: -24x + 2x2 = -36 Solving -24x + 2x2 = -36 Solving for variable 'x'. Reorder the terms: 36 + -24x + 2x2 = -36 + 36 Combine like terms: -36 + 36 = 0 36 + -24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + -12x + x2)' equal to zero and attempt to solve: Simplifying 18 + -12x + x2 = 0 Solving 18 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -12x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -12x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -12x + x2 = 0 + -18 -12x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -12x + x2 = -18 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -18 + 36 Reorder the terms: 36 + -12x + x2 = -18 + 36 Combine like terms: -18 + 36 = 18 36 + -12x + x2 = 18 Factor a perfect square on the left side: (x + -6)(x + -6) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -6) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -6 = 4.242640687 Simplifying x + -6 = 4.242640687 Reorder the terms: -6 + x = 4.242640687 Solving -6 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 4.242640687 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.242640687 + 6 x = 4.242640687 + 6 Combine like terms: 4.242640687 + 6 = 10.242640687 x = 10.242640687 Simplifying x = 10.242640687Subproblem 2
x + -6 = -4.242640687 Simplifying x + -6 = -4.242640687 Reorder the terms: -6 + x = -4.242640687 Solving -6 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -4.242640687 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.242640687 + 6 x = -4.242640687 + 6 Combine like terms: -4.242640687 + 6 = 1.757359313 x = 1.757359313 Simplifying x = 1.757359313Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.242640687, 1.757359313}Solution
x = {10.242640687, 1.757359313}
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