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Simplifying 2x2 + -46x + 13 = 0 Reorder the terms: 13 + -46x + 2x2 = 0 Solving 13 + -46x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -23x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -23x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -23x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -23x + x2 = 0 + -6.5 -23x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -23x + x2 = -6.5 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 = -6.5 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -6.5 + 132.25 Combine like terms: -6.5 + 132.25 = 125.75 132.25 + -23x + x2 = 125.75 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 125.75 Calculate the square root of the right side: 11.213830746 Break this problem into two subproblems by setting (x + -11.5) equal to 11.213830746 and -11.213830746.Subproblem 1
x + -11.5 = 11.213830746 Simplifying x + -11.5 = 11.213830746 Reorder the terms: -11.5 + x = 11.213830746 Solving -11.5 + x = 11.213830746 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 = 11.213830746 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.213830746 + 11.5 x = 11.213830746 + 11.5 Combine like terms: 11.213830746 + 11.5 = 22.713830746 x = 22.713830746 Simplifying x = 22.713830746Subproblem 2
x + -11.5 = -11.213830746 Simplifying x + -11.5 = -11.213830746 Reorder the terms: -11.5 + x = -11.213830746 Solving -11.5 + x = -11.213830746 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 = -11.213830746 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.213830746 + 11.5 x = -11.213830746 + 11.5 Combine like terms: -11.213830746 + 11.5 = 0.286169254 x = 0.286169254 Simplifying x = 0.286169254Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.713830746, 0.286169254}
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