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Simplifying 5x + -5 = 4x + -3x2 + 8 + -6x Reorder the terms: -5 + 5x = 4x + -3x2 + 8 + -6x Reorder the terms: -5 + 5x = 8 + 4x + -6x + -3x2 Combine like terms: 4x + -6x = -2x -5 + 5x = 8 + -2x + -3x2 Solving -5 + 5x = 8 + -2x + -3x2 Solving for variable 'x'. Reorder the terms: -5 + -8 + 5x + 2x + 3x2 = 8 + -2x + -3x2 + -8 + 2x + 3x2 Combine like terms: -5 + -8 = -13 -13 + 5x + 2x + 3x2 = 8 + -2x + -3x2 + -8 + 2x + 3x2 Combine like terms: 5x + 2x = 7x -13 + 7x + 3x2 = 8 + -2x + -3x2 + -8 + 2x + 3x2 Reorder the terms: -13 + 7x + 3x2 = 8 + -8 + -2x + 2x + -3x2 + 3x2 Combine like terms: 8 + -8 = 0 -13 + 7x + 3x2 = 0 + -2x + 2x + -3x2 + 3x2 -13 + 7x + 3x2 = -2x + 2x + -3x2 + 3x2 Combine like terms: -2x + 2x = 0 -13 + 7x + 3x2 = 0 + -3x2 + 3x2 -13 + 7x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -13 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.333333333 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + 2.333333333x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + 2.333333333x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + 2.333333333x + x2 = 0 + 4.333333333 2.333333333x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 2.333333333x + x2 = 4.333333333 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 4.333333333 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 4.333333333 + 1.361111112 Combine like terms: 4.333333333 + 1.361111112 = 5.694444445 1.361111112 + 2.333333333x + x2 = 5.694444445 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 5.694444445 Calculate the square root of the right side: 2.386303511 Break this problem into two subproblems by setting (x + 1.166666667) equal to 2.386303511 and -2.386303511.Subproblem 1
x + 1.166666667 = 2.386303511 Simplifying x + 1.166666667 = 2.386303511 Reorder the terms: 1.166666667 + x = 2.386303511 Solving 1.166666667 + x = 2.386303511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 2.386303511 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 2.386303511 + -1.166666667 x = 2.386303511 + -1.166666667 Combine like terms: 2.386303511 + -1.166666667 = 1.219636844 x = 1.219636844 Simplifying x = 1.219636844Subproblem 2
x + 1.166666667 = -2.386303511 Simplifying x + 1.166666667 = -2.386303511 Reorder the terms: 1.166666667 + x = -2.386303511 Solving 1.166666667 + x = -2.386303511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -2.386303511 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -2.386303511 + -1.166666667 x = -2.386303511 + -1.166666667 Combine like terms: -2.386303511 + -1.166666667 = -3.552970178 x = -3.552970178 Simplifying x = -3.552970178Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.219636844, -3.552970178}
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