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Simplifying -3x2 = 2(3x + -5) Reorder the terms: -3x2 = 2(-5 + 3x) -3x2 = (-5 * 2 + 3x * 2) -3x2 = (-10 + 6x) Solving -3x2 = -10 + 6x Solving for variable 'x'. Reorder the terms: 10 + -6x + -3x2 = -10 + 6x + 10 + -6x Reorder the terms: 10 + -6x + -3x2 = -10 + 10 + 6x + -6x Combine like terms: -10 + 10 = 0 10 + -6x + -3x2 = 0 + 6x + -6x 10 + -6x + -3x2 = 6x + -6x Combine like terms: 6x + -6x = 0 10 + -6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -3.333333333 + 2x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 2x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 2x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 2x + x2 = 0 + 3.333333333 2x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 2x + x2 = 3.333333333 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 = 3.333333333 + 1 Reorder the terms: 1 + 2x + x2 = 3.333333333 + 1 Combine like terms: 3.333333333 + 1 = 4.333333333 1 + 2x + x2 = 4.333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 4.333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (x + 1) equal to 2.081665999 and -2.081665999.Subproblem 1
x + 1 = 2.081665999 Simplifying x + 1 = 2.081665999 Reorder the terms: 1 + x = 2.081665999 Solving 1 + x = 2.081665999 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 = 2.081665999 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.081665999 + -1 x = 2.081665999 + -1 Combine like terms: 2.081665999 + -1 = 1.081665999 x = 1.081665999 Simplifying x = 1.081665999Subproblem 2
x + 1 = -2.081665999 Simplifying x + 1 = -2.081665999 Reorder the terms: 1 + x = -2.081665999 Solving 1 + x = -2.081665999 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 = -2.081665999 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.081665999 + -1 x = -2.081665999 + -1 Combine like terms: -2.081665999 + -1 = -3.081665999 x = -3.081665999 Simplifying x = -3.081665999Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.081665999, -3.081665999}
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