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Simplifying 9x2 + -75x + 4 = 0 Reorder the terms: 4 + -75x + 9x2 = 0 Solving 4 + -75x + 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 + -8.333333333x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -8.333333333x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -8.333333333x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -8.333333333x + x2 = 0 + -0.4444444444 -8.333333333x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -8.333333333x + x2 = -0.4444444444 The x term is -8.333333333x. Take half its coefficient (-4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. -8.333333333x + 17.36111111 + x2 = -0.4444444444 + 17.36111111 Reorder the terms: 17.36111111 + -8.333333333x + x2 = -0.4444444444 + 17.36111111 Combine like terms: -0.4444444444 + 17.36111111 = 16.9166666656 17.36111111 + -8.333333333x + x2 = 16.9166666656 Factor a perfect square on the left side: (x + -4.166666667)(x + -4.166666667) = 16.9166666656 Calculate the square root of the right side: 4.11298756 Break this problem into two subproblems by setting (x + -4.166666667) equal to 4.11298756 and -4.11298756.Subproblem 1
x + -4.166666667 = 4.11298756 Simplifying x + -4.166666667 = 4.11298756 Reorder the terms: -4.166666667 + x = 4.11298756 Solving -4.166666667 + x = 4.11298756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 4.11298756 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 4.11298756 + 4.166666667 x = 4.11298756 + 4.166666667 Combine like terms: 4.11298756 + 4.166666667 = 8.279654227 x = 8.279654227 Simplifying x = 8.279654227Subproblem 2
x + -4.166666667 = -4.11298756 Simplifying x + -4.166666667 = -4.11298756 Reorder the terms: -4.166666667 + x = -4.11298756 Solving -4.166666667 + x = -4.11298756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -4.11298756 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -4.11298756 + 4.166666667 x = -4.11298756 + 4.166666667 Combine like terms: -4.11298756 + 4.166666667 = 0.053679107 x = 0.053679107 Simplifying x = 0.053679107Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.279654227, 0.053679107}
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