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Simplifying 3x2 + -6x = 20 Reorder the terms: -6x + 3x2 = 20 Solving -6x + 3x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + -6x + 3x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.666666667 + -2x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -2x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -2x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -2x + x2 = 0 + 6.666666667 -2x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -2x + x2 = 6.666666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 6.666666667 + 1 Reorder the terms: 1 + -2x + x2 = 6.666666667 + 1 Combine like terms: 6.666666667 + 1 = 7.666666667 1 + -2x + x2 = 7.666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 7.666666667 Calculate the square root of the right side: 2.768874621 Break this problem into two subproblems by setting (x + -1) equal to 2.768874621 and -2.768874621.Subproblem 1
x + -1 = 2.768874621 Simplifying x + -1 = 2.768874621 Reorder the terms: -1 + x = 2.768874621 Solving -1 + x = 2.768874621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.768874621 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.768874621 + 1 x = 2.768874621 + 1 Combine like terms: 2.768874621 + 1 = 3.768874621 x = 3.768874621 Simplifying x = 3.768874621Subproblem 2
x + -1 = -2.768874621 Simplifying x + -1 = -2.768874621 Reorder the terms: -1 + x = -2.768874621 Solving -1 + x = -2.768874621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.768874621 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.768874621 + 1 x = -2.768874621 + 1 Combine like terms: -2.768874621 + 1 = -1.768874621 x = -1.768874621 Simplifying x = -1.768874621Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.768874621, -1.768874621}
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