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Simplifying (6.2x + -3.4)(0.7x + 1.3) = 0 Reorder the terms: (-3.4 + 6.2x)(0.7x + 1.3) = 0 Reorder the terms: (-3.4 + 6.2x)(1.3 + 0.7x) = 0 Multiply (-3.4 + 6.2x) * (1.3 + 0.7x) (-3.4(1.3 + 0.7x) + 6.2x * (1.3 + 0.7x)) = 0 ((1.3 * -3.4 + 0.7x * -3.4) + 6.2x * (1.3 + 0.7x)) = 0 ((-4.42 + -2.38x) + 6.2x * (1.3 + 0.7x)) = 0 (-4.42 + -2.38x + (1.3 * 6.2x + 0.7x * 6.2x)) = 0 (-4.42 + -2.38x + (8.06x + 4.34x2)) = 0 Combine like terms: -2.38x + 8.06x = 5.68x (-4.42 + 5.68x + 4.34x2) = 0 Solving -4.42 + 5.68x + 4.34x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.34 the coefficient of the squared term: Divide each side by '4.34'. -1.01843318 + 1.30875576x + x2 = 0 Move the constant term to the right: Add '1.01843318' to each side of the equation. -1.01843318 + 1.30875576x + 1.01843318 + x2 = 0 + 1.01843318 Reorder the terms: -1.01843318 + 1.01843318 + 1.30875576x + x2 = 0 + 1.01843318 Combine like terms: -1.01843318 + 1.01843318 = 0.00000000 0.00000000 + 1.30875576x + x2 = 0 + 1.01843318 1.30875576x + x2 = 0 + 1.01843318 Combine like terms: 0 + 1.01843318 = 1.01843318 1.30875576x + x2 = 1.01843318 The x term is 1.30875576x. Take half its coefficient (0.65437788). Square it (0.4282104098) and add it to both sides. Add '0.4282104098' to each side of the equation. 1.30875576x + 0.4282104098 + x2 = 1.01843318 + 0.4282104098 Reorder the terms: 0.4282104098 + 1.30875576x + x2 = 1.01843318 + 0.4282104098 Combine like terms: 1.01843318 + 0.4282104098 = 1.4466435898 0.4282104098 + 1.30875576x + x2 = 1.4466435898 Factor a perfect square on the left side: (x + 0.65437788)(x + 0.65437788) = 1.4466435898 Calculate the square root of the right side: 1.202764977 Break this problem into two subproblems by setting (x + 0.65437788) equal to 1.202764977 and -1.202764977.Subproblem 1
x + 0.65437788 = 1.202764977 Simplifying x + 0.65437788 = 1.202764977 Reorder the terms: 0.65437788 + x = 1.202764977 Solving 0.65437788 + x = 1.202764977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65437788' to each side of the equation. 0.65437788 + -0.65437788 + x = 1.202764977 + -0.65437788 Combine like terms: 0.65437788 + -0.65437788 = 0.00000000 0.00000000 + x = 1.202764977 + -0.65437788 x = 1.202764977 + -0.65437788 Combine like terms: 1.202764977 + -0.65437788 = 0.548387097 x = 0.548387097 Simplifying x = 0.548387097Subproblem 2
x + 0.65437788 = -1.202764977 Simplifying x + 0.65437788 = -1.202764977 Reorder the terms: 0.65437788 + x = -1.202764977 Solving 0.65437788 + x = -1.202764977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65437788' to each side of the equation. 0.65437788 + -0.65437788 + x = -1.202764977 + -0.65437788 Combine like terms: 0.65437788 + -0.65437788 = 0.00000000 0.00000000 + x = -1.202764977 + -0.65437788 x = -1.202764977 + -0.65437788 Combine like terms: -1.202764977 + -0.65437788 = -1.857142857 x = -1.857142857 Simplifying x = -1.857142857Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.548387097, -1.857142857}
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