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Simplifying 780 = 2x2 + 22x + 48 Reorder the terms: 780 = 48 + 22x + 2x2 Solving 780 = 48 + 22x + 2x2 Solving for variable 'x'. Combine like terms: 780 + -48 = 732 732 + -22x + -2x2 = 48 + 22x + 2x2 + -48 + -22x + -2x2 Reorder the terms: 732 + -22x + -2x2 = 48 + -48 + 22x + -22x + 2x2 + -2x2 Combine like terms: 48 + -48 = 0 732 + -22x + -2x2 = 0 + 22x + -22x + 2x2 + -2x2 732 + -22x + -2x2 = 22x + -22x + 2x2 + -2x2 Combine like terms: 22x + -22x = 0 732 + -22x + -2x2 = 0 + 2x2 + -2x2 732 + -22x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 732 + -22x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(366 + -11x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(366 + -11x + -1x2)' equal to zero and attempt to solve: Simplifying 366 + -11x + -1x2 = 0 Solving 366 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -366 + 11x + x2 = 0 Move the constant term to the right: Add '366' to each side of the equation. -366 + 11x + 366 + x2 = 0 + 366 Reorder the terms: -366 + 366 + 11x + x2 = 0 + 366 Combine like terms: -366 + 366 = 0 0 + 11x + x2 = 0 + 366 11x + x2 = 0 + 366 Combine like terms: 0 + 366 = 366 11x + x2 = 366 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 366 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 366 + 30.25 Combine like terms: 366 + 30.25 = 396.25 30.25 + 11x + x2 = 396.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 396.25 Calculate the square root of the right side: 19.906029237 Break this problem into two subproblems by setting (x + 5.5) equal to 19.906029237 and -19.906029237.Subproblem 1
x + 5.5 = 19.906029237 Simplifying x + 5.5 = 19.906029237 Reorder the terms: 5.5 + x = 19.906029237 Solving 5.5 + x = 19.906029237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 19.906029237 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 19.906029237 + -5.5 x = 19.906029237 + -5.5 Combine like terms: 19.906029237 + -5.5 = 14.406029237 x = 14.406029237 Simplifying x = 14.406029237Subproblem 2
x + 5.5 = -19.906029237 Simplifying x + 5.5 = -19.906029237 Reorder the terms: 5.5 + x = -19.906029237 Solving 5.5 + x = -19.906029237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -19.906029237 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -19.906029237 + -5.5 x = -19.906029237 + -5.5 Combine like terms: -19.906029237 + -5.5 = -25.406029237 x = -25.406029237 Simplifying x = -25.406029237Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.406029237, -25.406029237}Solution
x = {14.406029237, -25.406029237}
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