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Simplifying 0 = 9x2 + -62x + -50 Reorder the terms: 0 = -50 + -62x + 9x2 Solving 0 = -50 + -62x + 9x2 Solving for variable 'x'. Combine like terms: 0 + 50 = 50 50 + 62x + -9x2 = -50 + -62x + 9x2 + 50 + 62x + -9x2 Reorder the terms: 50 + 62x + -9x2 = -50 + 50 + -62x + 62x + 9x2 + -9x2 Combine like terms: -50 + 50 = 0 50 + 62x + -9x2 = 0 + -62x + 62x + 9x2 + -9x2 50 + 62x + -9x2 = -62x + 62x + 9x2 + -9x2 Combine like terms: -62x + 62x = 0 50 + 62x + -9x2 = 0 + 9x2 + -9x2 50 + 62x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 50 + 62x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -5.555555556 + -6.888888889x + x2 = 0 Move the constant term to the right: Add '5.555555556' to each side of the equation. -5.555555556 + -6.888888889x + 5.555555556 + x2 = 0 + 5.555555556 Reorder the terms: -5.555555556 + 5.555555556 + -6.888888889x + x2 = 0 + 5.555555556 Combine like terms: -5.555555556 + 5.555555556 = 0.000000000 0.000000000 + -6.888888889x + x2 = 0 + 5.555555556 -6.888888889x + x2 = 0 + 5.555555556 Combine like terms: 0 + 5.555555556 = 5.555555556 -6.888888889x + x2 = 5.555555556 The x term is -6.888888889x. Take half its coefficient (-3.444444445). Square it (11.86419753) and add it to both sides. Add '11.86419753' to each side of the equation. -6.888888889x + 11.86419753 + x2 = 5.555555556 + 11.86419753 Reorder the terms: 11.86419753 + -6.888888889x + x2 = 5.555555556 + 11.86419753 Combine like terms: 5.555555556 + 11.86419753 = 17.419753086 11.86419753 + -6.888888889x + x2 = 17.419753086 Factor a perfect square on the left side: (x + -3.444444445)(x + -3.444444445) = 17.419753086 Calculate the square root of the right side: 4.173697771 Break this problem into two subproblems by setting (x + -3.444444445) equal to 4.173697771 and -4.173697771.Subproblem 1
x + -3.444444445 = 4.173697771 Simplifying x + -3.444444445 = 4.173697771 Reorder the terms: -3.444444445 + x = 4.173697771 Solving -3.444444445 + x = 4.173697771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.444444445' to each side of the equation. -3.444444445 + 3.444444445 + x = 4.173697771 + 3.444444445 Combine like terms: -3.444444445 + 3.444444445 = 0.000000000 0.000000000 + x = 4.173697771 + 3.444444445 x = 4.173697771 + 3.444444445 Combine like terms: 4.173697771 + 3.444444445 = 7.618142216 x = 7.618142216 Simplifying x = 7.618142216Subproblem 2
x + -3.444444445 = -4.173697771 Simplifying x + -3.444444445 = -4.173697771 Reorder the terms: -3.444444445 + x = -4.173697771 Solving -3.444444445 + x = -4.173697771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.444444445' to each side of the equation. -3.444444445 + 3.444444445 + x = -4.173697771 + 3.444444445 Combine like terms: -3.444444445 + 3.444444445 = 0.000000000 0.000000000 + x = -4.173697771 + 3.444444445 x = -4.173697771 + 3.444444445 Combine like terms: -4.173697771 + 3.444444445 = -0.729253326 x = -0.729253326 Simplifying x = -0.729253326Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.618142216, -0.729253326}
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