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Simplifying 2x2 + 35x = 45 Reorder the terms: 35x + 2x2 = 45 Solving 35x + 2x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 35x + 2x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 35x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + 17.5x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 17.5x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 17.5x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 17.5x + x2 = 0 + 22.5 17.5x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 17.5x + x2 = 22.5 The x term is 17.5x. Take half its coefficient (8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. 17.5x + 76.5625 + x2 = 22.5 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 22.5 + 76.5625 Combine like terms: 22.5 + 76.5625 = 99.0625 76.5625 + 17.5x + x2 = 99.0625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 99.0625 Calculate the square root of the right side: 9.953014619 Break this problem into two subproblems by setting (x + 8.75) equal to 9.953014619 and -9.953014619.Subproblem 1
x + 8.75 = 9.953014619 Simplifying x + 8.75 = 9.953014619 Reorder the terms: 8.75 + x = 9.953014619 Solving 8.75 + x = 9.953014619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = 9.953014619 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 9.953014619 + -8.75 x = 9.953014619 + -8.75 Combine like terms: 9.953014619 + -8.75 = 1.203014619 x = 1.203014619 Simplifying x = 1.203014619Subproblem 2
x + 8.75 = -9.953014619 Simplifying x + 8.75 = -9.953014619 Reorder the terms: 8.75 + x = -9.953014619 Solving 8.75 + x = -9.953014619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = -9.953014619 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -9.953014619 + -8.75 x = -9.953014619 + -8.75 Combine like terms: -9.953014619 + -8.75 = -18.703014619 x = -18.703014619 Simplifying x = -18.703014619Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.203014619, -18.703014619}
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