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Simplifying 46x + -12 = x2 Reorder the terms: -12 + 46x = x2 Solving -12 + 46x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 -12 + 46x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -46x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -46x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -46x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -46x + x2 = 0 + -12 -46x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -46x + x2 = -12 The x term is -46x. Take half its coefficient (-23). Square it (529) and add it to both sides. Add '529' to each side of the equation. -46x + 529 + x2 = -12 + 529 Reorder the terms: 529 + -46x + x2 = -12 + 529 Combine like terms: -12 + 529 = 517 529 + -46x + x2 = 517 Factor a perfect square on the left side: (x + -23)(x + -23) = 517 Calculate the square root of the right side: 22.737634002 Break this problem into two subproblems by setting (x + -23) equal to 22.737634002 and -22.737634002.Subproblem 1
x + -23 = 22.737634002 Simplifying x + -23 = 22.737634002 Reorder the terms: -23 + x = 22.737634002 Solving -23 + x = 22.737634002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = 22.737634002 + 23 Combine like terms: -23 + 23 = 0 0 + x = 22.737634002 + 23 x = 22.737634002 + 23 Combine like terms: 22.737634002 + 23 = 45.737634002 x = 45.737634002 Simplifying x = 45.737634002Subproblem 2
x + -23 = -22.737634002 Simplifying x + -23 = -22.737634002 Reorder the terms: -23 + x = -22.737634002 Solving -23 + x = -22.737634002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = -22.737634002 + 23 Combine like terms: -23 + 23 = 0 0 + x = -22.737634002 + 23 x = -22.737634002 + 23 Combine like terms: -22.737634002 + 23 = 0.262365998 x = 0.262365998 Simplifying x = 0.262365998Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.737634002, 0.262365998}
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