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Simplifying 5x + 45(x2 + 5x) = 12x + 5 Reorder the terms: 5x + 45(5x + x2) = 12x + 5 5x + (5x * 45 + x2 * 45) = 12x + 5 5x + (225x + 45x2) = 12x + 5 Combine like terms: 5x + 225x = 230x 230x + 45x2 = 12x + 5 Reorder the terms: 230x + 45x2 = 5 + 12x Solving 230x + 45x2 = 5 + 12x Solving for variable 'x'. Reorder the terms: -5 + 230x + -12x + 45x2 = 5 + 12x + -5 + -12x Combine like terms: 230x + -12x = 218x -5 + 218x + 45x2 = 5 + 12x + -5 + -12x Reorder the terms: -5 + 218x + 45x2 = 5 + -5 + 12x + -12x Combine like terms: 5 + -5 = 0 -5 + 218x + 45x2 = 0 + 12x + -12x -5 + 218x + 45x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -5 + 218x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.1111111111 + 4.844444444x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 4.844444444x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 4.844444444x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 4.844444444x + x2 = 0 + 0.1111111111 4.844444444x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 4.844444444x + x2 = 0.1111111111 The x term is 4.844444444x. Take half its coefficient (2.422222222). Square it (5.867160493) and add it to both sides. Add '5.867160493' to each side of the equation. 4.844444444x + 5.867160493 + x2 = 0.1111111111 + 5.867160493 Reorder the terms: 5.867160493 + 4.844444444x + x2 = 0.1111111111 + 5.867160493 Combine like terms: 0.1111111111 + 5.867160493 = 5.9782716041 5.867160493 + 4.844444444x + x2 = 5.9782716041 Factor a perfect square on the left side: (x + 2.422222222)(x + 2.422222222) = 5.9782716041 Calculate the square root of the right side: 2.44505043 Break this problem into two subproblems by setting (x + 2.422222222) equal to 2.44505043 and -2.44505043.Subproblem 1
x + 2.422222222 = 2.44505043 Simplifying x + 2.422222222 = 2.44505043 Reorder the terms: 2.422222222 + x = 2.44505043 Solving 2.422222222 + x = 2.44505043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.422222222' to each side of the equation. 2.422222222 + -2.422222222 + x = 2.44505043 + -2.422222222 Combine like terms: 2.422222222 + -2.422222222 = 0.000000000 0.000000000 + x = 2.44505043 + -2.422222222 x = 2.44505043 + -2.422222222 Combine like terms: 2.44505043 + -2.422222222 = 0.022828208 x = 0.022828208 Simplifying x = 0.022828208Subproblem 2
x + 2.422222222 = -2.44505043 Simplifying x + 2.422222222 = -2.44505043 Reorder the terms: 2.422222222 + x = -2.44505043 Solving 2.422222222 + x = -2.44505043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.422222222' to each side of the equation. 2.422222222 + -2.422222222 + x = -2.44505043 + -2.422222222 Combine like terms: 2.422222222 + -2.422222222 = 0.000000000 0.000000000 + x = -2.44505043 + -2.422222222 x = -2.44505043 + -2.422222222 Combine like terms: -2.44505043 + -2.422222222 = -4.867272652 x = -4.867272652 Simplifying x = -4.867272652Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.022828208, -4.867272652}
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