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Simplifying 5x2 + -7x + -6 = 2x2 + -20x Reorder the terms: -6 + -7x + 5x2 = 2x2 + -20x Reorder the terms: -6 + -7x + 5x2 = -20x + 2x2 Solving -6 + -7x + 5x2 = -20x + 2x2 Solving for variable 'x'. Reorder the terms: -6 + -7x + 20x + 5x2 + -2x2 = -20x + 2x2 + 20x + -2x2 Combine like terms: -7x + 20x = 13x -6 + 13x + 5x2 + -2x2 = -20x + 2x2 + 20x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -6 + 13x + 3x2 = -20x + 2x2 + 20x + -2x2 Reorder the terms: -6 + 13x + 3x2 = -20x + 20x + 2x2 + -2x2 Combine like terms: -20x + 20x = 0 -6 + 13x + 3x2 = 0 + 2x2 + -2x2 -6 + 13x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + 13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 4.333333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 4.333333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 4.333333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4.333333333x + x2 = 0 + 2 4.333333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 4.333333333x + x2 = 2 The x term is 4.333333333x. Take half its coefficient (2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. 4.333333333x + 4.694444446 + x2 = 2 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333x + x2 = 2 + 4.694444446 Combine like terms: 2 + 4.694444446 = 6.694444446 4.694444446 + 4.333333333x + x2 = 6.694444446 Factor a perfect square on the left side: (x + 2.166666667)(x + 2.166666667) = 6.694444446 Calculate the square root of the right side: 2.58736245 Break this problem into two subproblems by setting (x + 2.166666667) equal to 2.58736245 and -2.58736245.Subproblem 1
x + 2.166666667 = 2.58736245 Simplifying x + 2.166666667 = 2.58736245 Reorder the terms: 2.166666667 + x = 2.58736245 Solving 2.166666667 + x = 2.58736245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = 2.58736245 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 2.58736245 + -2.166666667 x = 2.58736245 + -2.166666667 Combine like terms: 2.58736245 + -2.166666667 = 0.420695783 x = 0.420695783 Simplifying x = 0.420695783Subproblem 2
x + 2.166666667 = -2.58736245 Simplifying x + 2.166666667 = -2.58736245 Reorder the terms: 2.166666667 + x = -2.58736245 Solving 2.166666667 + x = -2.58736245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = -2.58736245 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -2.58736245 + -2.166666667 x = -2.58736245 + -2.166666667 Combine like terms: -2.58736245 + -2.166666667 = -4.754029117 x = -4.754029117 Simplifying x = -4.754029117Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.420695783, -4.754029117}
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