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Simplifying 45(x2) + -1 = 56x Reorder the terms: -1 + 45x2 = 56x Solving -1 + 45x2 = 56x Solving for variable 'x'. Reorder the terms: -1 + -56x + 45x2 = 56x + -56x Combine like terms: 56x + -56x = 0 -1 + -56x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.02222222222 + -1.244444444x + x2 = 0 Move the constant term to the right: Add '0.02222222222' to each side of the equation. -0.02222222222 + -1.244444444x + 0.02222222222 + x2 = 0 + 0.02222222222 Reorder the terms: -0.02222222222 + 0.02222222222 + -1.244444444x + x2 = 0 + 0.02222222222 Combine like terms: -0.02222222222 + 0.02222222222 = 0.00000000000 0.00000000000 + -1.244444444x + x2 = 0 + 0.02222222222 -1.244444444x + x2 = 0 + 0.02222222222 Combine like terms: 0 + 0.02222222222 = 0.02222222222 -1.244444444x + x2 = 0.02222222222 The x term is -1.244444444x. Take half its coefficient (-0.622222222). Square it (0.3871604936) and add it to both sides. Add '0.3871604936' to each side of the equation. -1.244444444x + 0.3871604936 + x2 = 0.02222222222 + 0.3871604936 Reorder the terms: 0.3871604936 + -1.244444444x + x2 = 0.02222222222 + 0.3871604936 Combine like terms: 0.02222222222 + 0.3871604936 = 0.40938271582 0.3871604936 + -1.244444444x + x2 = 0.40938271582 Factor a perfect square on the left side: (x + -0.622222222)(x + -0.622222222) = 0.40938271582 Calculate the square root of the right side: 0.639830224 Break this problem into two subproblems by setting (x + -0.622222222) equal to 0.639830224 and -0.639830224.Subproblem 1
x + -0.622222222 = 0.639830224 Simplifying x + -0.622222222 = 0.639830224 Reorder the terms: -0.622222222 + x = 0.639830224 Solving -0.622222222 + x = 0.639830224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.622222222' to each side of the equation. -0.622222222 + 0.622222222 + x = 0.639830224 + 0.622222222 Combine like terms: -0.622222222 + 0.622222222 = 0.000000000 0.000000000 + x = 0.639830224 + 0.622222222 x = 0.639830224 + 0.622222222 Combine like terms: 0.639830224 + 0.622222222 = 1.262052446 x = 1.262052446 Simplifying x = 1.262052446Subproblem 2
x + -0.622222222 = -0.639830224 Simplifying x + -0.622222222 = -0.639830224 Reorder the terms: -0.622222222 + x = -0.639830224 Solving -0.622222222 + x = -0.639830224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.622222222' to each side of the equation. -0.622222222 + 0.622222222 + x = -0.639830224 + 0.622222222 Combine like terms: -0.622222222 + 0.622222222 = 0.000000000 0.000000000 + x = -0.639830224 + 0.622222222 x = -0.639830224 + 0.622222222 Combine like terms: -0.639830224 + 0.622222222 = -0.017608002 x = -0.017608002 Simplifying x = -0.017608002Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.262052446, -0.017608002}
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