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Simplifying x2 + 37x + 70 = 106 Reorder the terms: 70 + 37x + x2 = 106 Solving 70 + 37x + x2 = 106 Solving for variable 'x'. Reorder the terms: 70 + -106 + 37x + x2 = 106 + -106 Combine like terms: 70 + -106 = -36 -36 + 37x + x2 = 106 + -106 Combine like terms: 106 + -106 = 0 -36 + 37x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 37x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 37x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 37x + x2 = 0 + 36 37x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 37x + x2 = 36 The x term is 37x. Take half its coefficient (18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. 37x + 342.25 + x2 = 36 + 342.25 Reorder the terms: 342.25 + 37x + x2 = 36 + 342.25 Combine like terms: 36 + 342.25 = 378.25 342.25 + 37x + x2 = 378.25 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 378.25 Calculate the square root of the right side: 19.448650339 Break this problem into two subproblems by setting (x + 18.5) equal to 19.448650339 and -19.448650339.Subproblem 1
x + 18.5 = 19.448650339 Simplifying x + 18.5 = 19.448650339 Reorder the terms: 18.5 + x = 19.448650339 Solving 18.5 + x = 19.448650339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = 19.448650339 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 19.448650339 + -18.5 x = 19.448650339 + -18.5 Combine like terms: 19.448650339 + -18.5 = 0.948650339 x = 0.948650339 Simplifying x = 0.948650339Subproblem 2
x + 18.5 = -19.448650339 Simplifying x + 18.5 = -19.448650339 Reorder the terms: 18.5 + x = -19.448650339 Solving 18.5 + x = -19.448650339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = -19.448650339 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -19.448650339 + -18.5 x = -19.448650339 + -18.5 Combine like terms: -19.448650339 + -18.5 = -37.948650339 x = -37.948650339 Simplifying x = -37.948650339Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.948650339, -37.948650339}
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