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Simplifying 9x2 + -62x + 7 = 0 Reorder the terms: 7 + -62x + 9x2 = 0 Solving 7 + -62x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.7777777778 + -6.888888889x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + -6.888888889x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + -6.888888889x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + -6.888888889x + x2 = 0 + -0.7777777778 -6.888888889x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 -6.888888889x + x2 = -0.7777777778 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 = -0.7777777778 + 11.86419753 Reorder the terms: 11.86419753 + -6.888888889x + x2 = -0.7777777778 + 11.86419753 Combine like terms: -0.7777777778 + 11.86419753 = 11.0864197522 11.86419753 + -6.888888889x + x2 = 11.0864197522 Factor a perfect square on the left side: (x + -3.444444445)(x + -3.444444445) = 11.0864197522 Calculate the square root of the right side: 3.32962757 Break this problem into two subproblems by setting (x + -3.444444445) equal to 3.32962757 and -3.32962757.Subproblem 1
x + -3.444444445 = 3.32962757 Simplifying x + -3.444444445 = 3.32962757 Reorder the terms: -3.444444445 + x = 3.32962757 Solving -3.444444445 + x = 3.32962757 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 = 3.32962757 + 3.444444445 Combine like terms: -3.444444445 + 3.444444445 = 0.000000000 0.000000000 + x = 3.32962757 + 3.444444445 x = 3.32962757 + 3.444444445 Combine like terms: 3.32962757 + 3.444444445 = 6.774072015 x = 6.774072015 Simplifying x = 6.774072015Subproblem 2
x + -3.444444445 = -3.32962757 Simplifying x + -3.444444445 = -3.32962757 Reorder the terms: -3.444444445 + x = -3.32962757 Solving -3.444444445 + x = -3.32962757 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 = -3.32962757 + 3.444444445 Combine like terms: -3.444444445 + 3.444444445 = 0.000000000 0.000000000 + x = -3.32962757 + 3.444444445 x = -3.32962757 + 3.444444445 Combine like terms: -3.32962757 + 3.444444445 = 0.114816875 x = 0.114816875 Simplifying x = 0.114816875Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.774072015, 0.114816875}
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