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Simplifying 2x2 + -24x + 38 = 0 Reorder the terms: 38 + -24x + 2x2 = 0 Solving 38 + -24x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(19 + -12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + -12x + x2)' equal to zero and attempt to solve: Simplifying 19 + -12x + x2 = 0 Solving 19 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -12x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + -12x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -12x + x2 = 0 + -19 -12x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 -12x + x2 = -19 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 = -19 + 36 Reorder the terms: 36 + -12x + x2 = -19 + 36 Combine like terms: -19 + 36 = 17 36 + -12x + x2 = 17 Factor a perfect square on the left side: (x + -6)(x + -6) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + -6) equal to 4.123105626 and -4.123105626.Subproblem 1
x + -6 = 4.123105626 Simplifying x + -6 = 4.123105626 Reorder the terms: -6 + x = 4.123105626 Solving -6 + x = 4.123105626 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 = 4.123105626 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.123105626 + 6 x = 4.123105626 + 6 Combine like terms: 4.123105626 + 6 = 10.123105626 x = 10.123105626 Simplifying x = 10.123105626Subproblem 2
x + -6 = -4.123105626 Simplifying x + -6 = -4.123105626 Reorder the terms: -6 + x = -4.123105626 Solving -6 + x = -4.123105626 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 = -4.123105626 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.123105626 + 6 x = -4.123105626 + 6 Combine like terms: -4.123105626 + 6 = 1.876894374 x = 1.876894374 Simplifying x = 1.876894374Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.123105626, 1.876894374}Solution
x = {10.123105626, 1.876894374}
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