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Simplifying 2334x + -334 = 345x2 Reorder the terms: -334 + 2334x = 345x2 Solving -334 + 2334x = 345x2 Solving for variable 'x'. Combine like terms: 345x2 + -345x2 = 0 -334 + 2334x + -345x2 = 0 Begin completing the square. Divide all terms by -345 the coefficient of the squared term: Divide each side by '-345'. 0.968115942 + -6.765217391x + x2 = 0 Move the constant term to the right: Add '-0.968115942' to each side of the equation. 0.968115942 + -6.765217391x + -0.968115942 + x2 = 0 + -0.968115942 Reorder the terms: 0.968115942 + -0.968115942 + -6.765217391x + x2 = 0 + -0.968115942 Combine like terms: 0.968115942 + -0.968115942 = 0.000000000 0.000000000 + -6.765217391x + x2 = 0 + -0.968115942 -6.765217391x + x2 = 0 + -0.968115942 Combine like terms: 0 + -0.968115942 = -0.968115942 -6.765217391x + x2 = -0.968115942 The x term is -6.765217391x. Take half its coefficient (-3.382608696). Square it (11.44204159) and add it to both sides. Add '11.44204159' to each side of the equation. -6.765217391x + 11.44204159 + x2 = -0.968115942 + 11.44204159 Reorder the terms: 11.44204159 + -6.765217391x + x2 = -0.968115942 + 11.44204159 Combine like terms: -0.968115942 + 11.44204159 = 10.473925648 11.44204159 + -6.765217391x + x2 = 10.473925648 Factor a perfect square on the left side: (x + -3.382608696)(x + -3.382608696) = 10.473925648 Calculate the square root of the right side: 3.236344488 Break this problem into two subproblems by setting (x + -3.382608696) equal to 3.236344488 and -3.236344488.Subproblem 1
x + -3.382608696 = 3.236344488 Simplifying x + -3.382608696 = 3.236344488 Reorder the terms: -3.382608696 + x = 3.236344488 Solving -3.382608696 + x = 3.236344488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.382608696' to each side of the equation. -3.382608696 + 3.382608696 + x = 3.236344488 + 3.382608696 Combine like terms: -3.382608696 + 3.382608696 = 0.000000000 0.000000000 + x = 3.236344488 + 3.382608696 x = 3.236344488 + 3.382608696 Combine like terms: 3.236344488 + 3.382608696 = 6.618953184 x = 6.618953184 Simplifying x = 6.618953184Subproblem 2
x + -3.382608696 = -3.236344488 Simplifying x + -3.382608696 = -3.236344488 Reorder the terms: -3.382608696 + x = -3.236344488 Solving -3.382608696 + x = -3.236344488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.382608696' to each side of the equation. -3.382608696 + 3.382608696 + x = -3.236344488 + 3.382608696 Combine like terms: -3.382608696 + 3.382608696 = 0.000000000 0.000000000 + x = -3.236344488 + 3.382608696 x = -3.236344488 + 3.382608696 Combine like terms: -3.236344488 + 3.382608696 = 0.146264208 x = 0.146264208 Simplifying x = 0.146264208Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.618953184, 0.146264208}
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