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Simplifying 3x2 + -69x + 16 = 0 Reorder the terms: 16 + -69x + 3x2 = 0 Solving 16 + -69x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.333333333 + -23x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + -23x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + -23x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + -23x + x2 = 0 + -5.333333333 -23x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 -23x + x2 = -5.333333333 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -5.333333333 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -5.333333333 + 132.25 Combine like terms: -5.333333333 + 132.25 = 126.916666667 132.25 + -23x + x2 = 126.916666667 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 126.916666667 Calculate the square root of the right side: 11.265729744 Break this problem into two subproblems by setting (x + -11.5) equal to 11.265729744 and -11.265729744.Subproblem 1
x + -11.5 = 11.265729744 Simplifying x + -11.5 = 11.265729744 Reorder the terms: -11.5 + x = 11.265729744 Solving -11.5 + x = 11.265729744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 11.265729744 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.265729744 + 11.5 x = 11.265729744 + 11.5 Combine like terms: 11.265729744 + 11.5 = 22.765729744 x = 22.765729744 Simplifying x = 22.765729744Subproblem 2
x + -11.5 = -11.265729744 Simplifying x + -11.5 = -11.265729744 Reorder the terms: -11.5 + x = -11.265729744 Solving -11.5 + x = -11.265729744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -11.265729744 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.265729744 + 11.5 x = -11.265729744 + 11.5 Combine like terms: -11.265729744 + 11.5 = 0.234270256 x = 0.234270256 Simplifying x = 0.234270256Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.765729744, 0.234270256}
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