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Simplifying 780 = 3x2 + -22x + 48 Reorder the terms: 780 = 48 + -22x + 3x2 Solving 780 = 48 + -22x + 3x2 Solving for variable 'x'. Combine like terms: 780 + -48 = 732 732 + 22x + -3x2 = 48 + -22x + 3x2 + -48 + 22x + -3x2 Reorder the terms: 732 + 22x + -3x2 = 48 + -48 + -22x + 22x + 3x2 + -3x2 Combine like terms: 48 + -48 = 0 732 + 22x + -3x2 = 0 + -22x + 22x + 3x2 + -3x2 732 + 22x + -3x2 = -22x + 22x + 3x2 + -3x2 Combine like terms: -22x + 22x = 0 732 + 22x + -3x2 = 0 + 3x2 + -3x2 732 + 22x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 732 + 22x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -244 + -7.333333333x + x2 = 0 Move the constant term to the right: Add '244' to each side of the equation. -244 + -7.333333333x + 244 + x2 = 0 + 244 Reorder the terms: -244 + 244 + -7.333333333x + x2 = 0 + 244 Combine like terms: -244 + 244 = 0 0 + -7.333333333x + x2 = 0 + 244 -7.333333333x + x2 = 0 + 244 Combine like terms: 0 + 244 = 244 -7.333333333x + x2 = 244 The x term is -7.333333333x. Take half its coefficient (-3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. -7.333333333x + 13.44444445 + x2 = 244 + 13.44444445 Reorder the terms: 13.44444445 + -7.333333333x + x2 = 244 + 13.44444445 Combine like terms: 244 + 13.44444445 = 257.44444445 13.44444445 + -7.333333333x + x2 = 257.44444445 Factor a perfect square on the left side: (x + -3.666666667)(x + -3.666666667) = 257.44444445 Calculate the square root of the right side: 16.045075396 Break this problem into two subproblems by setting (x + -3.666666667) equal to 16.045075396 and -16.045075396.Subproblem 1
x + -3.666666667 = 16.045075396 Simplifying x + -3.666666667 = 16.045075396 Reorder the terms: -3.666666667 + x = 16.045075396 Solving -3.666666667 + x = 16.045075396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + x = 16.045075396 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = 16.045075396 + 3.666666667 x = 16.045075396 + 3.666666667 Combine like terms: 16.045075396 + 3.666666667 = 19.711742063 x = 19.711742063 Simplifying x = 19.711742063Subproblem 2
x + -3.666666667 = -16.045075396 Simplifying x + -3.666666667 = -16.045075396 Reorder the terms: -3.666666667 + x = -16.045075396 Solving -3.666666667 + x = -16.045075396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + x = -16.045075396 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = -16.045075396 + 3.666666667 x = -16.045075396 + 3.666666667 Combine like terms: -16.045075396 + 3.666666667 = -12.378408729 x = -12.378408729 Simplifying x = -12.378408729Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.711742063, -12.378408729}
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