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Simplifying -5.2x2 + 65x + -75 = 0 Reorder the terms: -75 + 65x + -5.2x2 = 0 Solving -75 + 65x + -5.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5.2 the coefficient of the squared term: Divide each side by '-5.2'. 14.42307692 + -12.5x + x2 = 0 Move the constant term to the right: Add '-14.42307692' to each side of the equation. 14.42307692 + -12.5x + -14.42307692 + x2 = 0 + -14.42307692 Reorder the terms: 14.42307692 + -14.42307692 + -12.5x + x2 = 0 + -14.42307692 Combine like terms: 14.42307692 + -14.42307692 = 0.00000000 0.00000000 + -12.5x + x2 = 0 + -14.42307692 -12.5x + x2 = 0 + -14.42307692 Combine like terms: 0 + -14.42307692 = -14.42307692 -12.5x + x2 = -14.42307692 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -14.42307692 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -14.42307692 + 39.0625 Combine like terms: -14.42307692 + 39.0625 = 24.63942308 39.0625 + -12.5x + x2 = 24.63942308 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 24.63942308 Calculate the square root of the right side: 4.963811346 Break this problem into two subproblems by setting (x + -6.25) equal to 4.963811346 and -4.963811346.Subproblem 1
x + -6.25 = 4.963811346 Simplifying x + -6.25 = 4.963811346 Reorder the terms: -6.25 + x = 4.963811346 Solving -6.25 + x = 4.963811346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 4.963811346 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 4.963811346 + 6.25 x = 4.963811346 + 6.25 Combine like terms: 4.963811346 + 6.25 = 11.213811346 x = 11.213811346 Simplifying x = 11.213811346Subproblem 2
x + -6.25 = -4.963811346 Simplifying x + -6.25 = -4.963811346 Reorder the terms: -6.25 + x = -4.963811346 Solving -6.25 + x = -4.963811346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -4.963811346 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -4.963811346 + 6.25 x = -4.963811346 + 6.25 Combine like terms: -4.963811346 + 6.25 = 1.286188654 x = 1.286188654 Simplifying x = 1.286188654Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.213811346, 1.286188654}
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