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Simplifying 6x2 + -44x = -63 Reorder the terms: -44x + 6x2 = -63 Solving -44x + 6x2 = -63 Solving for variable 'x'. Reorder the terms: 63 + -44x + 6x2 = -63 + 63 Combine like terms: -63 + 63 = 0 63 + -44x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 10.5 + -7.333333333x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -7.333333333x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -7.333333333x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -7.333333333x + x2 = 0 + -10.5 -7.333333333x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -7.333333333x + x2 = -10.5 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 = -10.5 + 13.44444445 Reorder the terms: 13.44444445 + -7.333333333x + x2 = -10.5 + 13.44444445 Combine like terms: -10.5 + 13.44444445 = 2.94444445 13.44444445 + -7.333333333x + x2 = 2.94444445 Factor a perfect square on the left side: (x + -3.666666667)(x + -3.666666667) = 2.94444445 Calculate the square root of the right side: 1.715938358 Break this problem into two subproblems by setting (x + -3.666666667) equal to 1.715938358 and -1.715938358.Subproblem 1
x + -3.666666667 = 1.715938358 Simplifying x + -3.666666667 = 1.715938358 Reorder the terms: -3.666666667 + x = 1.715938358 Solving -3.666666667 + x = 1.715938358 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 = 1.715938358 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = 1.715938358 + 3.666666667 x = 1.715938358 + 3.666666667 Combine like terms: 1.715938358 + 3.666666667 = 5.382605025 x = 5.382605025 Simplifying x = 5.382605025Subproblem 2
x + -3.666666667 = -1.715938358 Simplifying x + -3.666666667 = -1.715938358 Reorder the terms: -3.666666667 + x = -1.715938358 Solving -3.666666667 + x = -1.715938358 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 = -1.715938358 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = -1.715938358 + 3.666666667 x = -1.715938358 + 3.666666667 Combine like terms: -1.715938358 + 3.666666667 = 1.950728309 x = 1.950728309 Simplifying x = 1.950728309Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.382605025, 1.950728309}
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