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Simplifying 8 + 7(3 + -6x) * x = 3 Reorder the terms for easier multiplication: 8 + 7x(3 + -6x) = 3 8 + (3 * 7x + -6x * 7x) = 3 8 + (21x + -42x2) = 3 Solving 8 + 21x + -42x2 = 3 Solving for variable 'x'. Reorder the terms: 8 + -3 + 21x + -42x2 = 3 + -3 Combine like terms: 8 + -3 = 5 5 + 21x + -42x2 = 3 + -3 Combine like terms: 3 + -3 = 0 5 + 21x + -42x2 = 0 Begin completing the square. Divide all terms by -42 the coefficient of the squared term: Divide each side by '-42'. -0.119047619 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.119047619' to each side of the equation. -0.119047619 + -0.5x + 0.119047619 + x2 = 0 + 0.119047619 Reorder the terms: -0.119047619 + 0.119047619 + -0.5x + x2 = 0 + 0.119047619 Combine like terms: -0.119047619 + 0.119047619 = 0.000000000 0.000000000 + -0.5x + x2 = 0 + 0.119047619 -0.5x + x2 = 0 + 0.119047619 Combine like terms: 0 + 0.119047619 = 0.119047619 -0.5x + x2 = 0.119047619 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.119047619 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.119047619 + 0.0625 Combine like terms: 0.119047619 + 0.0625 = 0.181547619 0.0625 + -0.5x + x2 = 0.181547619 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.181547619 Calculate the square root of the right side: 0.426084052 Break this problem into two subproblems by setting (x + -0.25) equal to 0.426084052 and -0.426084052.Subproblem 1
x + -0.25 = 0.426084052 Simplifying x + -0.25 = 0.426084052 Reorder the terms: -0.25 + x = 0.426084052 Solving -0.25 + x = 0.426084052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.426084052 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.426084052 + 0.25 x = 0.426084052 + 0.25 Combine like terms: 0.426084052 + 0.25 = 0.676084052 x = 0.676084052 Simplifying x = 0.676084052Subproblem 2
x + -0.25 = -0.426084052 Simplifying x + -0.25 = -0.426084052 Reorder the terms: -0.25 + x = -0.426084052 Solving -0.25 + x = -0.426084052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.426084052 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.426084052 + 0.25 x = -0.426084052 + 0.25 Combine like terms: -0.426084052 + 0.25 = -0.176084052 x = -0.176084052 Simplifying x = -0.176084052Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.676084052, -0.176084052}
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