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Simplifying 6x + 8x2 = 26x3 Solving 6x + 8x2 = 26x3 Solving for variable 'x'. Combine like terms: 26x3 + -26x3 = 0 6x + 8x2 + -26x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + 4x + -13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(3 + 4x + -13x2)' equal to zero and attempt to solve: Simplifying 3 + 4x + -13x2 = 0 Solving 3 + 4x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.2307692308 + -0.3076923077x + x2 = 0 Move the constant term to the right: Add '0.2307692308' to each side of the equation. -0.2307692308 + -0.3076923077x + 0.2307692308 + x2 = 0 + 0.2307692308 Reorder the terms: -0.2307692308 + 0.2307692308 + -0.3076923077x + x2 = 0 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + -0.3076923077x + x2 = 0 + 0.2307692308 -0.3076923077x + x2 = 0 + 0.2307692308 Combine like terms: 0 + 0.2307692308 = 0.2307692308 -0.3076923077x + x2 = 0.2307692308 The x term is -0.3076923077x. Take half its coefficient (-0.1538461539). Square it (0.02366863907) and add it to both sides. Add '0.02366863907' to each side of the equation. -0.3076923077x + 0.02366863907 + x2 = 0.2307692308 + 0.02366863907 Reorder the terms: 0.02366863907 + -0.3076923077x + x2 = 0.2307692308 + 0.02366863907 Combine like terms: 0.2307692308 + 0.02366863907 = 0.25443786987 0.02366863907 + -0.3076923077x + x2 = 0.25443786987 Factor a perfect square on the left side: (x + -0.1538461539)(x + -0.1538461539) = 0.25443786987 Calculate the square root of the right side: 0.504418348 Break this problem into two subproblems by setting (x + -0.1538461539) equal to 0.504418348 and -0.504418348.Subproblem 1
x + -0.1538461539 = 0.504418348 Simplifying x + -0.1538461539 = 0.504418348 Reorder the terms: -0.1538461539 + x = 0.504418348 Solving -0.1538461539 + x = 0.504418348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + x = 0.504418348 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = 0.504418348 + 0.1538461539 x = 0.504418348 + 0.1538461539 Combine like terms: 0.504418348 + 0.1538461539 = 0.6582645019 x = 0.6582645019 Simplifying x = 0.6582645019Subproblem 2
x + -0.1538461539 = -0.504418348 Simplifying x + -0.1538461539 = -0.504418348 Reorder the terms: -0.1538461539 + x = -0.504418348 Solving -0.1538461539 + x = -0.504418348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + x = -0.504418348 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = -0.504418348 + 0.1538461539 x = -0.504418348 + 0.1538461539 Combine like terms: -0.504418348 + 0.1538461539 = -0.3505721941 x = -0.3505721941 Simplifying x = -0.3505721941Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6582645019, -0.3505721941}Solution
x = {0, 0.6582645019, -0.3505721941}
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