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Simplifying x + 8(12 + -1x) = 7x(5x + -42) x + (12 * 8 + -1x * 8) = 7x(5x + -42) x + (96 + -8x) = 7x(5x + -42) Reorder the terms: 96 + x + -8x = 7x(5x + -42) Combine like terms: x + -8x = -7x 96 + -7x = 7x(5x + -42) Reorder the terms: 96 + -7x = 7x(-42 + 5x) 96 + -7x = (-42 * 7x + 5x * 7x) 96 + -7x = (-294x + 35x2) Solving 96 + -7x = -294x + 35x2 Solving for variable 'x'. Combine like terms: -7x + 294x = 287x 96 + 287x + -35x2 = -294x + 35x2 + 294x + -35x2 Reorder the terms: 96 + 287x + -35x2 = -294x + 294x + 35x2 + -35x2 Combine like terms: -294x + 294x = 0 96 + 287x + -35x2 = 0 + 35x2 + -35x2 96 + 287x + -35x2 = 35x2 + -35x2 Combine like terms: 35x2 + -35x2 = 0 96 + 287x + -35x2 = 0 Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. -2.742857143 + -8.2x + x2 = 0 Move the constant term to the right: Add '2.742857143' to each side of the equation. -2.742857143 + -8.2x + 2.742857143 + x2 = 0 + 2.742857143 Reorder the terms: -2.742857143 + 2.742857143 + -8.2x + x2 = 0 + 2.742857143 Combine like terms: -2.742857143 + 2.742857143 = 0.000000000 0.000000000 + -8.2x + x2 = 0 + 2.742857143 -8.2x + x2 = 0 + 2.742857143 Combine like terms: 0 + 2.742857143 = 2.742857143 -8.2x + x2 = 2.742857143 The x term is -8.2x. Take half its coefficient (-4.1). Square it (16.81) and add it to both sides. Add '16.81' to each side of the equation. -8.2x + 16.81 + x2 = 2.742857143 + 16.81 Reorder the terms: 16.81 + -8.2x + x2 = 2.742857143 + 16.81 Combine like terms: 2.742857143 + 16.81 = 19.552857143 16.81 + -8.2x + x2 = 19.552857143 Factor a perfect square on the left side: (x + -4.1)(x + -4.1) = 19.552857143 Calculate the square root of the right side: 4.421861276 Break this problem into two subproblems by setting (x + -4.1) equal to 4.421861276 and -4.421861276.Subproblem 1
x + -4.1 = 4.421861276 Simplifying x + -4.1 = 4.421861276 Reorder the terms: -4.1 + x = 4.421861276 Solving -4.1 + x = 4.421861276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.1' to each side of the equation. -4.1 + 4.1 + x = 4.421861276 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + x = 4.421861276 + 4.1 x = 4.421861276 + 4.1 Combine like terms: 4.421861276 + 4.1 = 8.521861276 x = 8.521861276 Simplifying x = 8.521861276Subproblem 2
x + -4.1 = -4.421861276 Simplifying x + -4.1 = -4.421861276 Reorder the terms: -4.1 + x = -4.421861276 Solving -4.1 + x = -4.421861276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.1' to each side of the equation. -4.1 + 4.1 + x = -4.421861276 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + x = -4.421861276 + 4.1 x = -4.421861276 + 4.1 Combine like terms: -4.421861276 + 4.1 = -0.321861276 x = -0.321861276 Simplifying x = -0.321861276Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.521861276, -0.321861276}
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