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Simplifying 6x2 + 105x = 37 Reorder the terms: 105x + 6x2 = 37 Solving 105x + 6x2 = 37 Solving for variable 'x'. Reorder the terms: -37 + 105x + 6x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + 105x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6.166666667 + 17.5x + x2 = 0 Move the constant term to the right: Add '6.166666667' to each side of the equation. -6.166666667 + 17.5x + 6.166666667 + x2 = 0 + 6.166666667 Reorder the terms: -6.166666667 + 6.166666667 + 17.5x + x2 = 0 + 6.166666667 Combine like terms: -6.166666667 + 6.166666667 = 0.000000000 0.000000000 + 17.5x + x2 = 0 + 6.166666667 17.5x + x2 = 0 + 6.166666667 Combine like terms: 0 + 6.166666667 = 6.166666667 17.5x + x2 = 6.166666667 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 = 6.166666667 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 6.166666667 + 76.5625 Combine like terms: 6.166666667 + 76.5625 = 82.729166667 76.5625 + 17.5x + x2 = 82.729166667 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 82.729166667 Calculate the square root of the right side: 9.095557524 Break this problem into two subproblems by setting (x + 8.75) equal to 9.095557524 and -9.095557524.Subproblem 1
x + 8.75 = 9.095557524 Simplifying x + 8.75 = 9.095557524 Reorder the terms: 8.75 + x = 9.095557524 Solving 8.75 + x = 9.095557524 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 = 9.095557524 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 9.095557524 + -8.75 x = 9.095557524 + -8.75 Combine like terms: 9.095557524 + -8.75 = 0.345557524 x = 0.345557524 Simplifying x = 0.345557524Subproblem 2
x + 8.75 = -9.095557524 Simplifying x + 8.75 = -9.095557524 Reorder the terms: 8.75 + x = -9.095557524 Solving 8.75 + x = -9.095557524 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 = -9.095557524 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -9.095557524 + -8.75 x = -9.095557524 + -8.75 Combine like terms: -9.095557524 + -8.75 = -17.845557524 x = -17.845557524 Simplifying x = -17.845557524Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.345557524, -17.845557524}
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