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Simplifying (3x2 + -5x + 13) + (6x + -5 + -6x2) + -1(4 + -5x + 10x2) = 0 Reorder the terms: (13 + -5x + 3x2) + (6x + -5 + -6x2) + -1(4 + -5x + 10x2) = 0 Remove parenthesis around (13 + -5x + 3x2) 13 + -5x + 3x2 + (6x + -5 + -6x2) + -1(4 + -5x + 10x2) = 0 Reorder the terms: 13 + -5x + 3x2 + (-5 + 6x + -6x2) + -1(4 + -5x + 10x2) = 0 Remove parenthesis around (-5 + 6x + -6x2) 13 + -5x + 3x2 + -5 + 6x + -6x2 + -1(4 + -5x + 10x2) = 0 13 + -5x + 3x2 + -5 + 6x + -6x2 + (4 * -1 + -5x * -1 + 10x2 * -1) = 0 13 + -5x + 3x2 + -5 + 6x + -6x2 + (-4 + 5x + -10x2) = 0 Reorder the terms: 13 + -5 + -4 + -5x + 6x + 5x + 3x2 + -6x2 + -10x2 = 0 Combine like terms: 13 + -5 = 8 8 + -4 + -5x + 6x + 5x + 3x2 + -6x2 + -10x2 = 0 Combine like terms: 8 + -4 = 4 4 + -5x + 6x + 5x + 3x2 + -6x2 + -10x2 = 0 Combine like terms: -5x + 6x = 1x 4 + 1x + 5x + 3x2 + -6x2 + -10x2 = 0 Combine like terms: 1x + 5x = 6x 4 + 6x + 3x2 + -6x2 + -10x2 = 0 Combine like terms: 3x2 + -6x2 = -3x2 4 + 6x + -3x2 + -10x2 = 0 Combine like terms: -3x2 + -10x2 = -13x2 4 + 6x + -13x2 = 0 Solving 4 + 6x + -13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.3076923077 + -0.4615384615x + x2 = 0 Move the constant term to the right: Add '0.3076923077' to each side of the equation. -0.3076923077 + -0.4615384615x + 0.3076923077 + x2 = 0 + 0.3076923077 Reorder the terms: -0.3076923077 + 0.3076923077 + -0.4615384615x + x2 = 0 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + -0.4615384615x + x2 = 0 + 0.3076923077 -0.4615384615x + x2 = 0 + 0.3076923077 Combine like terms: 0 + 0.3076923077 = 0.3076923077 -0.4615384615x + x2 = 0.3076923077 The x term is -0.4615384615x. Take half its coefficient (-0.2307692308). Square it (0.05325443788) and add it to both sides. Add '0.05325443788' to each side of the equation. -0.4615384615x + 0.05325443788 + x2 = 0.3076923077 + 0.05325443788 Reorder the terms: 0.05325443788 + -0.4615384615x + x2 = 0.3076923077 + 0.05325443788 Combine like terms: 0.3076923077 + 0.05325443788 = 0.36094674558 0.05325443788 + -0.4615384615x + x2 = 0.36094674558 Factor a perfect square on the left side: (x + -0.2307692308)(x + -0.2307692308) = 0.36094674558 Calculate the square root of the right side: 0.600788437 Break this problem into two subproblems by setting (x + -0.2307692308) equal to 0.600788437 and -0.600788437.Subproblem 1
x + -0.2307692308 = 0.600788437 Simplifying x + -0.2307692308 = 0.600788437 Reorder the terms: -0.2307692308 + x = 0.600788437 Solving -0.2307692308 + x = 0.600788437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2307692308' to each side of the equation. -0.2307692308 + 0.2307692308 + x = 0.600788437 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + x = 0.600788437 + 0.2307692308 x = 0.600788437 + 0.2307692308 Combine like terms: 0.600788437 + 0.2307692308 = 0.8315576678 x = 0.8315576678 Simplifying x = 0.8315576678Subproblem 2
x + -0.2307692308 = -0.600788437 Simplifying x + -0.2307692308 = -0.600788437 Reorder the terms: -0.2307692308 + x = -0.600788437 Solving -0.2307692308 + x = -0.600788437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2307692308' to each side of the equation. -0.2307692308 + 0.2307692308 + x = -0.600788437 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + x = -0.600788437 + 0.2307692308 x = -0.600788437 + 0.2307692308 Combine like terms: -0.600788437 + 0.2307692308 = -0.3700192062 x = -0.3700192062 Simplifying x = -0.3700192062Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8315576678, -0.3700192062}
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