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Simplifying 13x2 + -5x = 6 + -2x2 Reorder the terms: -5x + 13x2 = 6 + -2x2 Solving -5x + 13x2 = 6 + -2x2 Solving for variable 'x'. Reorder the terms: -6 + -5x + 13x2 + 2x2 = 6 + -2x2 + -6 + 2x2 Combine like terms: 13x2 + 2x2 = 15x2 -6 + -5x + 15x2 = 6 + -2x2 + -6 + 2x2 Reorder the terms: -6 + -5x + 15x2 = 6 + -6 + -2x2 + 2x2 Combine like terms: 6 + -6 = 0 -6 + -5x + 15x2 = 0 + -2x2 + 2x2 -6 + -5x + 15x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -6 + -5x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.4 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.3333333333x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.3333333333x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.3333333333x + x2 = 0 + 0.4 -0.3333333333x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.3333333333x + x2 = 0.4 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 0.4 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 0.4 + 0.02777777779 Combine like terms: 0.4 + 0.02777777779 = 0.42777777779 0.02777777779 + -0.3333333333x + x2 = 0.42777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 0.42777777779 Calculate the square root of the right side: 0.654047229 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 0.654047229 and -0.654047229.Subproblem 1
x + -0.1666666667 = 0.654047229 Simplifying x + -0.1666666667 = 0.654047229 Reorder the terms: -0.1666666667 + x = 0.654047229 Solving -0.1666666667 + x = 0.654047229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 0.654047229 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.654047229 + 0.1666666667 x = 0.654047229 + 0.1666666667 Combine like terms: 0.654047229 + 0.1666666667 = 0.8207138957 x = 0.8207138957 Simplifying x = 0.8207138957Subproblem 2
x + -0.1666666667 = -0.654047229 Simplifying x + -0.1666666667 = -0.654047229 Reorder the terms: -0.1666666667 + x = -0.654047229 Solving -0.1666666667 + x = -0.654047229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -0.654047229 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.654047229 + 0.1666666667 x = -0.654047229 + 0.1666666667 Combine like terms: -0.654047229 + 0.1666666667 = -0.4873805623 x = -0.4873805623 Simplifying x = -0.4873805623Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8207138957, -0.4873805623}
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