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Simplifying 2x2 + 104 = 51x Reorder the terms: 104 + 2x2 = 51x Solving 104 + 2x2 = 51x Solving for variable 'x'. Reorder the terms: 104 + -51x + 2x2 = 51x + -51x Combine like terms: 51x + -51x = 0 104 + -51x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 52 + -25.5x + x2 = 0 Move the constant term to the right: Add '-52' to each side of the equation. 52 + -25.5x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + -25.5x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -25.5x + x2 = 0 + -52 -25.5x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 -25.5x + x2 = -52 The x term is -25.5x. Take half its coefficient (-12.75). Square it (162.5625) and add it to both sides. Add '162.5625' to each side of the equation. -25.5x + 162.5625 + x2 = -52 + 162.5625 Reorder the terms: 162.5625 + -25.5x + x2 = -52 + 162.5625 Combine like terms: -52 + 162.5625 = 110.5625 162.5625 + -25.5x + x2 = 110.5625 Factor a perfect square on the left side: (x + -12.75)(x + -12.75) = 110.5625 Calculate the square root of the right side: 10.514870422 Break this problem into two subproblems by setting (x + -12.75) equal to 10.514870422 and -10.514870422.Subproblem 1
x + -12.75 = 10.514870422 Simplifying x + -12.75 = 10.514870422 Reorder the terms: -12.75 + x = 10.514870422 Solving -12.75 + x = 10.514870422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.75' to each side of the equation. -12.75 + 12.75 + x = 10.514870422 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + x = 10.514870422 + 12.75 x = 10.514870422 + 12.75 Combine like terms: 10.514870422 + 12.75 = 23.264870422 x = 23.264870422 Simplifying x = 23.264870422Subproblem 2
x + -12.75 = -10.514870422 Simplifying x + -12.75 = -10.514870422 Reorder the terms: -12.75 + x = -10.514870422 Solving -12.75 + x = -10.514870422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.75' to each side of the equation. -12.75 + 12.75 + x = -10.514870422 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + x = -10.514870422 + 12.75 x = -10.514870422 + 12.75 Combine like terms: -10.514870422 + 12.75 = 2.235129578 x = 2.235129578 Simplifying x = 2.235129578Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.264870422, 2.235129578}
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