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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 = 10871.5625 10764.0625 + -207.5x + x2 = 10871.5625 Factor a perfect square on the left side: (x + -103.75)(x + -103.75) = 10871.5625 Calculate the square root of the right side: 104.266785219 Break this problem into two subproblems by setting (x + -103.75) equal to 104.266785219 and -104.266785219.Subproblem 1
x + -103.75 = 104.266785219 Simplifying x + -103.75 = 104.266785219 Reorder the terms: -103.75 + x = 104.266785219 Solving -103.75 + x = 104.266785219 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 = 104.266785219 + 103.75 Combine like terms: -103.75 + 103.75 = 0.00 0.00 + x = 104.266785219 + 103.75 x = 104.266785219 + 103.75 Combine like terms: 104.266785219 + 103.75 = 208.016785219 x = 208.016785219 Simplifying x = 208.016785219Subproblem 2
x + -103.75 = -104.266785219 Simplifying x + -103.75 = -104.266785219 Reorder the terms: -103.75 + x = -104.266785219 Solving -103.75 + x = -104.266785219 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 = -104.266785219 + 103.75 Combine like terms: -103.75 + 103.75 = 0.00 0.00 + x = -104.266785219 + 103.75 x = -104.266785219 + 103.75 Combine like terms: -104.266785219 + 103.75 = -0.516785219 x = -0.516785219 Simplifying x = -0.516785219Solution
The solution to the problem is based on the solutions from the subproblems. x = {208.016785219, -0.516785219}
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