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Simplifying 9x2 + -48x + 64 = 3 Reorder the terms: 64 + -48x + 9x2 = 3 Solving 64 + -48x + 9x2 = 3 Solving for variable 'x'. Reorder the terms: 64 + -3 + -48x + 9x2 = 3 + -3 Combine like terms: 64 + -3 = 61 61 + -48x + 9x2 = 3 + -3 Combine like terms: 3 + -3 = 0 61 + -48x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 6.777777778 + -5.333333333x + x2 = 0 Move the constant term to the right: Add '-6.777777778' to each side of the equation. 6.777777778 + -5.333333333x + -6.777777778 + x2 = 0 + -6.777777778 Reorder the terms: 6.777777778 + -6.777777778 + -5.333333333x + x2 = 0 + -6.777777778 Combine like terms: 6.777777778 + -6.777777778 = 0.000000000 0.000000000 + -5.333333333x + x2 = 0 + -6.777777778 -5.333333333x + x2 = 0 + -6.777777778 Combine like terms: 0 + -6.777777778 = -6.777777778 -5.333333333x + x2 = -6.777777778 The x term is -5.333333333x. Take half its coefficient (-2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. -5.333333333x + 7.111111113 + x2 = -6.777777778 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333x + x2 = -6.777777778 + 7.111111113 Combine like terms: -6.777777778 + 7.111111113 = 0.333333335 7.111111113 + -5.333333333x + x2 = 0.333333335 Factor a perfect square on the left side: (x + -2.666666667)(x + -2.666666667) = 0.333333335 Calculate the square root of the right side: 0.577350271 Break this problem into two subproblems by setting (x + -2.666666667) equal to 0.577350271 and -0.577350271.Subproblem 1
x + -2.666666667 = 0.577350271 Simplifying x + -2.666666667 = 0.577350271 Reorder the terms: -2.666666667 + x = 0.577350271 Solving -2.666666667 + x = 0.577350271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x = 0.577350271 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = 0.577350271 + 2.666666667 x = 0.577350271 + 2.666666667 Combine like terms: 0.577350271 + 2.666666667 = 3.244016938 x = 3.244016938 Simplifying x = 3.244016938Subproblem 2
x + -2.666666667 = -0.577350271 Simplifying x + -2.666666667 = -0.577350271 Reorder the terms: -2.666666667 + x = -0.577350271 Solving -2.666666667 + x = -0.577350271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x = -0.577350271 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = -0.577350271 + 2.666666667 x = -0.577350271 + 2.666666667 Combine like terms: -0.577350271 + 2.666666667 = 2.089316396 x = 2.089316396 Simplifying x = 2.089316396Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.244016938, 2.089316396}
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