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Simplifying 7x2 = 37x + 5 Reorder the terms: 7x2 = 5 + 37x Solving 7x2 = 5 + 37x Solving for variable 'x'. Reorder the terms: -5 + -37x + 7x2 = 5 + 37x + -5 + -37x Reorder the terms: -5 + -37x + 7x2 = 5 + -5 + 37x + -37x Combine like terms: 5 + -5 = 0 -5 + -37x + 7x2 = 0 + 37x + -37x -5 + -37x + 7x2 = 37x + -37x Combine like terms: 37x + -37x = 0 -5 + -37x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + -5.285714286x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -5.285714286x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -5.285714286x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -5.285714286x + x2 = 0 + 0.7142857143 -5.285714286x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -5.285714286x + x2 = 0.7142857143 The x term is -5.285714286x. Take half its coefficient (-2.642857143). Square it (6.984693878) and add it to both sides. Add '6.984693878' to each side of the equation. -5.285714286x + 6.984693878 + x2 = 0.7142857143 + 6.984693878 Reorder the terms: 6.984693878 + -5.285714286x + x2 = 0.7142857143 + 6.984693878 Combine like terms: 0.7142857143 + 6.984693878 = 7.6989795923 6.984693878 + -5.285714286x + x2 = 7.6989795923 Factor a perfect square on the left side: (x + -2.642857143)(x + -2.642857143) = 7.6989795923 Calculate the square root of the right side: 2.774703514 Break this problem into two subproblems by setting (x + -2.642857143) equal to 2.774703514 and -2.774703514.Subproblem 1
x + -2.642857143 = 2.774703514 Simplifying x + -2.642857143 = 2.774703514 Reorder the terms: -2.642857143 + x = 2.774703514 Solving -2.642857143 + x = 2.774703514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.642857143' to each side of the equation. -2.642857143 + 2.642857143 + x = 2.774703514 + 2.642857143 Combine like terms: -2.642857143 + 2.642857143 = 0.000000000 0.000000000 + x = 2.774703514 + 2.642857143 x = 2.774703514 + 2.642857143 Combine like terms: 2.774703514 + 2.642857143 = 5.417560657 x = 5.417560657 Simplifying x = 5.417560657Subproblem 2
x + -2.642857143 = -2.774703514 Simplifying x + -2.642857143 = -2.774703514 Reorder the terms: -2.642857143 + x = -2.774703514 Solving -2.642857143 + x = -2.774703514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.642857143' to each side of the equation. -2.642857143 + 2.642857143 + x = -2.774703514 + 2.642857143 Combine like terms: -2.642857143 + 2.642857143 = 0.000000000 0.000000000 + x = -2.774703514 + 2.642857143 x = -2.774703514 + 2.642857143 Combine like terms: -2.774703514 + 2.642857143 = -0.131846371 x = -0.131846371 Simplifying x = -0.131846371Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.417560657, -0.131846371}
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