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Simplifying 4x2 + -38x + 47 = 2 Reorder the terms: 47 + -38x + 4x2 = 2 Solving 47 + -38x + 4x2 = 2 Solving for variable 'x'. Reorder the terms: 47 + -2 + -38x + 4x2 = 2 + -2 Combine like terms: 47 + -2 = 45 45 + -38x + 4x2 = 2 + -2 Combine like terms: 2 + -2 = 0 45 + -38x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 11.25 + -9.5x + x2 = 0 Move the constant term to the right: Add '-11.25' to each side of the equation. 11.25 + -9.5x + -11.25 + x2 = 0 + -11.25 Reorder the terms: 11.25 + -11.25 + -9.5x + x2 = 0 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + -9.5x + x2 = 0 + -11.25 -9.5x + x2 = 0 + -11.25 Combine like terms: 0 + -11.25 = -11.25 -9.5x + x2 = -11.25 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = -11.25 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = -11.25 + 22.5625 Combine like terms: -11.25 + 22.5625 = 11.3125 22.5625 + -9.5x + x2 = 11.3125 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 11.3125 Calculate the square root of the right side: 3.363406012 Break this problem into two subproblems by setting (x + -4.75) equal to 3.363406012 and -3.363406012.Subproblem 1
x + -4.75 = 3.363406012 Simplifying x + -4.75 = 3.363406012 Reorder the terms: -4.75 + x = 3.363406012 Solving -4.75 + x = 3.363406012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 3.363406012 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 3.363406012 + 4.75 x = 3.363406012 + 4.75 Combine like terms: 3.363406012 + 4.75 = 8.113406012 x = 8.113406012 Simplifying x = 8.113406012Subproblem 2
x + -4.75 = -3.363406012 Simplifying x + -4.75 = -3.363406012 Reorder the terms: -4.75 + x = -3.363406012 Solving -4.75 + x = -3.363406012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -3.363406012 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -3.363406012 + 4.75 x = -3.363406012 + 4.75 Combine like terms: -3.363406012 + 4.75 = 1.386593988 x = 1.386593988 Simplifying x = 1.386593988Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.113406012, 1.386593988}
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