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Simplifying 3x + 226 = 7x(x + -6) Reorder the terms: 226 + 3x = 7x(x + -6) Reorder the terms: 226 + 3x = 7x(-6 + x) 226 + 3x = (-6 * 7x + x * 7x) 226 + 3x = (-42x + 7x2) Solving 226 + 3x = -42x + 7x2 Solving for variable 'x'. Combine like terms: 3x + 42x = 45x 226 + 45x + -7x2 = -42x + 7x2 + 42x + -7x2 Reorder the terms: 226 + 45x + -7x2 = -42x + 42x + 7x2 + -7x2 Combine like terms: -42x + 42x = 0 226 + 45x + -7x2 = 0 + 7x2 + -7x2 226 + 45x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 226 + 45x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -32.28571429 + -6.428571429x + x2 = 0 Move the constant term to the right: Add '32.28571429' to each side of the equation. -32.28571429 + -6.428571429x + 32.28571429 + x2 = 0 + 32.28571429 Reorder the terms: -32.28571429 + 32.28571429 + -6.428571429x + x2 = 0 + 32.28571429 Combine like terms: -32.28571429 + 32.28571429 = 0.00000000 0.00000000 + -6.428571429x + x2 = 0 + 32.28571429 -6.428571429x + x2 = 0 + 32.28571429 Combine like terms: 0 + 32.28571429 = 32.28571429 -6.428571429x + x2 = 32.28571429 The x term is -6.428571429x. Take half its coefficient (-3.214285715). Square it (10.33163266) and add it to both sides. Add '10.33163266' to each side of the equation. -6.428571429x + 10.33163266 + x2 = 32.28571429 + 10.33163266 Reorder the terms: 10.33163266 + -6.428571429x + x2 = 32.28571429 + 10.33163266 Combine like terms: 32.28571429 + 10.33163266 = 42.61734695 10.33163266 + -6.428571429x + x2 = 42.61734695 Factor a perfect square on the left side: (x + -3.214285715)(x + -3.214285715) = 42.61734695 Calculate the square root of the right side: 6.528196301 Break this problem into two subproblems by setting (x + -3.214285715) equal to 6.528196301 and -6.528196301.Subproblem 1
x + -3.214285715 = 6.528196301 Simplifying x + -3.214285715 = 6.528196301 Reorder the terms: -3.214285715 + x = 6.528196301 Solving -3.214285715 + x = 6.528196301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.214285715' to each side of the equation. -3.214285715 + 3.214285715 + x = 6.528196301 + 3.214285715 Combine like terms: -3.214285715 + 3.214285715 = 0.000000000 0.000000000 + x = 6.528196301 + 3.214285715 x = 6.528196301 + 3.214285715 Combine like terms: 6.528196301 + 3.214285715 = 9.742482016 x = 9.742482016 Simplifying x = 9.742482016Subproblem 2
x + -3.214285715 = -6.528196301 Simplifying x + -3.214285715 = -6.528196301 Reorder the terms: -3.214285715 + x = -6.528196301 Solving -3.214285715 + x = -6.528196301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.214285715' to each side of the equation. -3.214285715 + 3.214285715 + x = -6.528196301 + 3.214285715 Combine like terms: -3.214285715 + 3.214285715 = 0.000000000 0.000000000 + x = -6.528196301 + 3.214285715 x = -6.528196301 + 3.214285715 Combine like terms: -6.528196301 + 3.214285715 = -3.313910586 x = -3.313910586 Simplifying x = -3.313910586Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.742482016, -3.313910586}
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