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Simplifying -16x2 + 4928x + -720 = 0 Reorder the terms: -720 + 4928x + -16x2 = 0 Solving -720 + 4928x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(-45 + 308x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-45 + 308x + -1x2)' equal to zero and attempt to solve: Simplifying -45 + 308x + -1x2 = 0 Solving -45 + 308x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 45 + -308x + x2 = 0 Move the constant term to the right: Add '-45' to each side of the equation. 45 + -308x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -308x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -308x + x2 = 0 + -45 -308x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -308x + x2 = -45 The x term is -308x. Take half its coefficient (-154). Square it (23716) and add it to both sides. Add '23716' to each side of the equation. -308x + 23716 + x2 = -45 + 23716 Reorder the terms: 23716 + -308x + x2 = -45 + 23716 Combine like terms: -45 + 23716 = 23671 23716 + -308x + x2 = 23671 Factor a perfect square on the left side: (x + -154)(x + -154) = 23671 Calculate the square root of the right side: 153.853826732 Break this problem into two subproblems by setting (x + -154) equal to 153.853826732 and -153.853826732.Subproblem 1
x + -154 = 153.853826732 Simplifying x + -154 = 153.853826732 Reorder the terms: -154 + x = 153.853826732 Solving -154 + x = 153.853826732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '154' to each side of the equation. -154 + 154 + x = 153.853826732 + 154 Combine like terms: -154 + 154 = 0 0 + x = 153.853826732 + 154 x = 153.853826732 + 154 Combine like terms: 153.853826732 + 154 = 307.853826732 x = 307.853826732 Simplifying x = 307.853826732Subproblem 2
x + -154 = -153.853826732 Simplifying x + -154 = -153.853826732 Reorder the terms: -154 + x = -153.853826732 Solving -154 + x = -153.853826732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '154' to each side of the equation. -154 + 154 + x = -153.853826732 + 154 Combine like terms: -154 + 154 = 0 0 + x = -153.853826732 + 154 x = -153.853826732 + 154 Combine like terms: -153.853826732 + 154 = 0.146173268 x = 0.146173268 Simplifying x = 0.146173268Solution
The solution to the problem is based on the solutions from the subproblems. x = {307.853826732, 0.146173268}Solution
x = {307.853826732, 0.146173268}
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