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Simplifying 45x2 + -40x + -1 = 0 Reorder the terms: -1 + -40x + 45x2 = 0 Solving -1 + -40x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.02222222222 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.02222222222' to each side of the equation. -0.02222222222 + -0.8888888889x + 0.02222222222 + x2 = 0 + 0.02222222222 Reorder the terms: -0.02222222222 + 0.02222222222 + -0.8888888889x + x2 = 0 + 0.02222222222 Combine like terms: -0.02222222222 + 0.02222222222 = 0.00000000000 0.00000000000 + -0.8888888889x + x2 = 0 + 0.02222222222 -0.8888888889x + x2 = 0 + 0.02222222222 Combine like terms: 0 + 0.02222222222 = 0.02222222222 -0.8888888889x + x2 = 0.02222222222 The x term is -0.8888888889x. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889x + 0.1975308642 + x2 = 0.02222222222 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 0.02222222222 + 0.1975308642 Combine like terms: 0.02222222222 + 0.1975308642 = 0.21975308642 0.1975308642 + -0.8888888889x + x2 = 0.21975308642 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 0.21975308642 Calculate the square root of the right side: 0.468778291 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 0.468778291 and -0.468778291.Subproblem 1
x + -0.4444444445 = 0.468778291 Simplifying x + -0.4444444445 = 0.468778291 Reorder the terms: -0.4444444445 + x = 0.468778291 Solving -0.4444444445 + x = 0.468778291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 0.468778291 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 0.468778291 + 0.4444444445 x = 0.468778291 + 0.4444444445 Combine like terms: 0.468778291 + 0.4444444445 = 0.9132227355 x = 0.9132227355 Simplifying x = 0.9132227355Subproblem 2
x + -0.4444444445 = -0.468778291 Simplifying x + -0.4444444445 = -0.468778291 Reorder the terms: -0.4444444445 + x = -0.468778291 Solving -0.4444444445 + x = -0.468778291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -0.468778291 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -0.468778291 + 0.4444444445 x = -0.468778291 + 0.4444444445 Combine like terms: -0.468778291 + 0.4444444445 = -0.0243338465 x = -0.0243338465 Simplifying x = -0.0243338465Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9132227355, -0.0243338465}
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