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Simplifying (3x2) + -2(3x) = 35 Remove parenthesis around (3x) (3x2) + -2 * 3x = 35 Multiply -2 * 3 (3x2) + -6x = 35 Reorder the terms: -6x + (3x2) = 35 Solving -6x + (3x2) = 35 Solving for variable 'x'. Reorder the terms: -35 + -6x + (3x2) = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -6x + (3x2) = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11.66666667 + -2x + x2 = 0 Move the constant term to the right: Add '11.66666667' to each side of the equation. -11.66666667 + -2x + 11.66666667 + x2 = 0 + 11.66666667 Reorder the terms: -11.66666667 + 11.66666667 + -2x + x2 = 0 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + -2x + x2 = 0 + 11.66666667 -2x + x2 = 0 + 11.66666667 Combine like terms: 0 + 11.66666667 = 11.66666667 -2x + x2 = 11.66666667 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 = 11.66666667 + 1 Reorder the terms: 1 + -2x + x2 = 11.66666667 + 1 Combine like terms: 11.66666667 + 1 = 12.66666667 1 + -2x + x2 = 12.66666667 Factor a perfect square on the left side: ((x) + -1)((x) + -1) = 12.66666667 Calculate the square root of the right side: 3.559026084 Break this problem into two subproblems by setting ((x) + -1) equal to 3.559026084 and -3.559026084.Subproblem 1
(x) + -1 = 3.559026084 Simplifying (x) + -1 = 3.559026084 x + -1 = 3.559026084 Reorder the terms: -1 + x = 3.559026084 Solving -1 + x = 3.559026084 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 = 3.559026084 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.559026084 + 1 x = 3.559026084 + 1 Combine like terms: 3.559026084 + 1 = 4.559026084 x = 4.559026084 Simplifying x = 4.559026084Subproblem 2
(x) + -1 = -3.559026084 Simplifying (x) + -1 = -3.559026084 x + -1 = -3.559026084 Reorder the terms: -1 + x = -3.559026084 Solving -1 + x = -3.559026084 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 = -3.559026084 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.559026084 + 1 x = -3.559026084 + 1 Combine like terms: -3.559026084 + 1 = -2.559026084 x = -2.559026084 Simplifying x = -2.559026084Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.559026084, -2.559026084}
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