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Simplifying 0.04x2 + 8.3x + 4.3 = 0 Reorder the terms: 4.3 + 8.3x + 0.04x2 = 0 Solving 4.3 + 8.3x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 107.5 + 207.5x + x2 = 0 Move the constant term to the right: Add '-107.5' to each side of the equation. 107.5 + 207.5x + -107.5 + x2 = 0 + -107.5 Reorder the terms: 107.5 + -107.5 + 207.5x + x2 = 0 + -107.5 Combine like terms: 107.5 + -107.5 = 0.0 0.0 + 207.5x + x2 = 0 + -107.5 207.5x + x2 = 0 + -107.5 Combine like terms: 0 + -107.5 = -107.5 207.5x + x2 = -107.5 The x term is 207.5x. Take half its coefficient (103.75). Square it (10764.0625) and add it to both sides. Add '10764.0625' to each side of the equation. 207.5x + 10764.0625 + x2 = -107.5 + 10764.0625 Reorder the terms: 10764.0625 + 207.5x + x2 = -107.5 + 10764.0625 Combine like terms: -107.5 + 10764.0625 = 10656.5625 10764.0625 + 207.5x + x2 = 10656.5625 Factor a perfect square on the left side: (x + 103.75)(x + 103.75) = 10656.5625 Calculate the square root of the right side: 103.230627723 Break this problem into two subproblems by setting (x + 103.75) equal to 103.230627723 and -103.230627723.Subproblem 1
x + 103.75 = 103.230627723 Simplifying x + 103.75 = 103.230627723 Reorder the terms: 103.75 + x = 103.230627723 Solving 103.75 + x = 103.230627723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-103.75' to each side of the equation. 103.75 + -103.75 + x = 103.230627723 + -103.75 Combine like terms: 103.75 + -103.75 = 0.00 0.00 + x = 103.230627723 + -103.75 x = 103.230627723 + -103.75 Combine like terms: 103.230627723 + -103.75 = -0.519372277 x = -0.519372277 Simplifying x = -0.519372277Subproblem 2
x + 103.75 = -103.230627723 Simplifying x + 103.75 = -103.230627723 Reorder the terms: 103.75 + x = -103.230627723 Solving 103.75 + x = -103.230627723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-103.75' to each side of the equation. 103.75 + -103.75 + x = -103.230627723 + -103.75 Combine like terms: 103.75 + -103.75 = 0.00 0.00 + x = -103.230627723 + -103.75 x = -103.230627723 + -103.75 Combine like terms: -103.230627723 + -103.75 = -206.980627723 x = -206.980627723 Simplifying x = -206.980627723Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.519372277, -206.980627723}
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