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Simplifying 9x2 + -35x + 4 = 0 Reorder the terms: 4 + -35x + 9x2 = 0 Solving 4 + -35x + 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'. 0.4444444444 + -3.888888889x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -3.888888889x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -3.888888889x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -3.888888889x + x2 = 0 + -0.4444444444 -3.888888889x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -3.888888889x + x2 = -0.4444444444 The x term is -3.888888889x. Take half its coefficient (-1.944444445). Square it (3.780864200) and add it to both sides. Add '3.780864200' to each side of the equation. -3.888888889x + 3.780864200 + x2 = -0.4444444444 + 3.780864200 Reorder the terms: 3.780864200 + -3.888888889x + x2 = -0.4444444444 + 3.780864200 Combine like terms: -0.4444444444 + 3.780864200 = 3.3364197556 3.780864200 + -3.888888889x + x2 = 3.3364197556 Factor a perfect square on the left side: (x + -1.944444445)(x + -1.944444445) = 3.3364197556 Calculate the square root of the right side: 1.826586914 Break this problem into two subproblems by setting (x + -1.944444445) equal to 1.826586914 and -1.826586914.Subproblem 1
x + -1.944444445 = 1.826586914 Simplifying x + -1.944444445 = 1.826586914 Reorder the terms: -1.944444445 + x = 1.826586914 Solving -1.944444445 + x = 1.826586914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.944444445' to each side of the equation. -1.944444445 + 1.944444445 + x = 1.826586914 + 1.944444445 Combine like terms: -1.944444445 + 1.944444445 = 0.000000000 0.000000000 + x = 1.826586914 + 1.944444445 x = 1.826586914 + 1.944444445 Combine like terms: 1.826586914 + 1.944444445 = 3.771031359 x = 3.771031359 Simplifying x = 3.771031359Subproblem 2
x + -1.944444445 = -1.826586914 Simplifying x + -1.944444445 = -1.826586914 Reorder the terms: -1.944444445 + x = -1.826586914 Solving -1.944444445 + x = -1.826586914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.944444445' to each side of the equation. -1.944444445 + 1.944444445 + x = -1.826586914 + 1.944444445 Combine like terms: -1.944444445 + 1.944444445 = 0.000000000 0.000000000 + x = -1.826586914 + 1.944444445 x = -1.826586914 + 1.944444445 Combine like terms: -1.826586914 + 1.944444445 = 0.117857531 x = 0.117857531 Simplifying x = 0.117857531Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.771031359, 0.117857531}
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