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Simplifying 19x2 + -836x + 3169 = 0 Reorder the terms: 3169 + -836x + 19x2 = 0 Solving 3169 + -836x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. 166.7894737 + -44x + x2 = 0 Move the constant term to the right: Add '-166.7894737' to each side of the equation. 166.7894737 + -44x + -166.7894737 + x2 = 0 + -166.7894737 Reorder the terms: 166.7894737 + -166.7894737 + -44x + x2 = 0 + -166.7894737 Combine like terms: 166.7894737 + -166.7894737 = 0.0000000 0.0000000 + -44x + x2 = 0 + -166.7894737 -44x + x2 = 0 + -166.7894737 Combine like terms: 0 + -166.7894737 = -166.7894737 -44x + x2 = -166.7894737 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = -166.7894737 + 484 Reorder the terms: 484 + -44x + x2 = -166.7894737 + 484 Combine like terms: -166.7894737 + 484 = 317.2105263 484 + -44x + x2 = 317.2105263 Factor a perfect square on the left side: (x + -22)(x + -22) = 317.2105263 Calculate the square root of the right side: 17.810405001 Break this problem into two subproblems by setting (x + -22) equal to 17.810405001 and -17.810405001.Subproblem 1
x + -22 = 17.810405001 Simplifying x + -22 = 17.810405001 Reorder the terms: -22 + x = 17.810405001 Solving -22 + x = 17.810405001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 17.810405001 + 22 Combine like terms: -22 + 22 = 0 0 + x = 17.810405001 + 22 x = 17.810405001 + 22 Combine like terms: 17.810405001 + 22 = 39.810405001 x = 39.810405001 Simplifying x = 39.810405001Subproblem 2
x + -22 = -17.810405001 Simplifying x + -22 = -17.810405001 Reorder the terms: -22 + x = -17.810405001 Solving -22 + x = -17.810405001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -17.810405001 + 22 Combine like terms: -22 + 22 = 0 0 + x = -17.810405001 + 22 x = -17.810405001 + 22 Combine like terms: -17.810405001 + 22 = 4.189594999 x = 4.189594999 Simplifying x = 4.189594999Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.810405001, 4.189594999}
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