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Simplifying 0 = 2x2 + -76x + 392 Reorder the terms: 0 = 392 + -76x + 2x2 Solving 0 = 392 + -76x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -392 = -392 -392 + 76x + -2x2 = 392 + -76x + 2x2 + -392 + 76x + -2x2 Reorder the terms: -392 + 76x + -2x2 = 392 + -392 + -76x + 76x + 2x2 + -2x2 Combine like terms: 392 + -392 = 0 -392 + 76x + -2x2 = 0 + -76x + 76x + 2x2 + -2x2 -392 + 76x + -2x2 = -76x + 76x + 2x2 + -2x2 Combine like terms: -76x + 76x = 0 -392 + 76x + -2x2 = 0 + 2x2 + -2x2 -392 + 76x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -392 + 76x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-196 + 38x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-196 + 38x + -1x2)' equal to zero and attempt to solve: Simplifying -196 + 38x + -1x2 = 0 Solving -196 + 38x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 196 + -38x + x2 = 0 Move the constant term to the right: Add '-196' to each side of the equation. 196 + -38x + -196 + x2 = 0 + -196 Reorder the terms: 196 + -196 + -38x + x2 = 0 + -196 Combine like terms: 196 + -196 = 0 0 + -38x + x2 = 0 + -196 -38x + x2 = 0 + -196 Combine like terms: 0 + -196 = -196 -38x + x2 = -196 The x term is -38x. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38x + 361 + x2 = -196 + 361 Reorder the terms: 361 + -38x + x2 = -196 + 361 Combine like terms: -196 + 361 = 165 361 + -38x + x2 = 165 Factor a perfect square on the left side: (x + -19)(x + -19) = 165 Calculate the square root of the right side: 12.845232579 Break this problem into two subproblems by setting (x + -19) equal to 12.845232579 and -12.845232579.Subproblem 1
x + -19 = 12.845232579 Simplifying x + -19 = 12.845232579 Reorder the terms: -19 + x = 12.845232579 Solving -19 + x = 12.845232579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 12.845232579 + 19 Combine like terms: -19 + 19 = 0 0 + x = 12.845232579 + 19 x = 12.845232579 + 19 Combine like terms: 12.845232579 + 19 = 31.845232579 x = 31.845232579 Simplifying x = 31.845232579Subproblem 2
x + -19 = -12.845232579 Simplifying x + -19 = -12.845232579 Reorder the terms: -19 + x = -12.845232579 Solving -19 + x = -12.845232579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = -12.845232579 + 19 Combine like terms: -19 + 19 = 0 0 + x = -12.845232579 + 19 x = -12.845232579 + 19 Combine like terms: -12.845232579 + 19 = 6.154767421 x = 6.154767421 Simplifying x = 6.154767421Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.845232579, 6.154767421}Solution
x = {31.845232579, 6.154767421}
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