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Simplifying (6x + 2x + -2) + -1(5x2 + -8x + -6) = 0 Reorder the terms: (-2 + 6x + 2x) + -1(5x2 + -8x + -6) = 0 Combine like terms: 6x + 2x = 8x (-2 + 8x) + -1(5x2 + -8x + -6) = 0 Remove parenthesis around (-2 + 8x) -2 + 8x + -1(5x2 + -8x + -6) = 0 Reorder the terms: -2 + 8x + -1(-6 + -8x + 5x2) = 0 -2 + 8x + (-6 * -1 + -8x * -1 + 5x2 * -1) = 0 -2 + 8x + (6 + 8x + -5x2) = 0 Reorder the terms: -2 + 6 + 8x + 8x + -5x2 = 0 Combine like terms: -2 + 6 = 4 4 + 8x + 8x + -5x2 = 0 Combine like terms: 8x + 8x = 16x 4 + 16x + -5x2 = 0 Solving 4 + 16x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.8 + -3.2x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -3.2x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -3.2x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -3.2x + x2 = 0 + 0.8 -3.2x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -3.2x + x2 = 0.8 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 0.8 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 0.8 + 2.56 Combine like terms: 0.8 + 2.56 = 3.36 2.56 + -3.2x + x2 = 3.36 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 3.36 Calculate the square root of the right side: 1.833030278 Break this problem into two subproblems by setting (x + -1.6) equal to 1.833030278 and -1.833030278.Subproblem 1
x + -1.6 = 1.833030278 Simplifying x + -1.6 = 1.833030278 Reorder the terms: -1.6 + x = 1.833030278 Solving -1.6 + x = 1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 1.833030278 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 1.833030278 + 1.6 x = 1.833030278 + 1.6 Combine like terms: 1.833030278 + 1.6 = 3.433030278 x = 3.433030278 Simplifying x = 3.433030278Subproblem 2
x + -1.6 = -1.833030278 Simplifying x + -1.6 = -1.833030278 Reorder the terms: -1.6 + x = -1.833030278 Solving -1.6 + x = -1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -1.833030278 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -1.833030278 + 1.6 x = -1.833030278 + 1.6 Combine like terms: -1.833030278 + 1.6 = -0.233030278 x = -0.233030278 Simplifying x = -0.233030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.433030278, -0.233030278}
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