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Simplifying -3x2 + 620x + 14 = 0 Reorder the terms: 14 + 620x + -3x2 = 0 Solving 14 + 620x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -4.666666667 + -206.6666667x + x2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + -206.6666667x + 4.666666667 + x2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + -206.6666667x + x2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + -206.6666667x + x2 = 0 + 4.666666667 -206.6666667x + x2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 -206.6666667x + x2 = 4.666666667 The x term is -206.6666667x. Take half its coefficient (-103.3333334). Square it (10677.77779) and add it to both sides. Add '10677.77779' to each side of the equation. -206.6666667x + 10677.77779 + x2 = 4.666666667 + 10677.77779 Reorder the terms: 10677.77779 + -206.6666667x + x2 = 4.666666667 + 10677.77779 Combine like terms: 4.666666667 + 10677.77779 = 10682.444456667 10677.77779 + -206.6666667x + x2 = 10682.444456667 Factor a perfect square on the left side: (x + -103.3333334)(x + -103.3333334) = 10682.444456667 Calculate the square root of the right side: 103.355911571 Break this problem into two subproblems by setting (x + -103.3333334) equal to 103.355911571 and -103.355911571.Subproblem 1
x + -103.3333334 = 103.355911571 Simplifying x + -103.3333334 = 103.355911571 Reorder the terms: -103.3333334 + x = 103.355911571 Solving -103.3333334 + x = 103.355911571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '103.3333334' to each side of the equation. -103.3333334 + 103.3333334 + x = 103.355911571 + 103.3333334 Combine like terms: -103.3333334 + 103.3333334 = 0.0000000 0.0000000 + x = 103.355911571 + 103.3333334 x = 103.355911571 + 103.3333334 Combine like terms: 103.355911571 + 103.3333334 = 206.689244971 x = 206.689244971 Simplifying x = 206.689244971Subproblem 2
x + -103.3333334 = -103.355911571 Simplifying x + -103.3333334 = -103.355911571 Reorder the terms: -103.3333334 + x = -103.355911571 Solving -103.3333334 + x = -103.355911571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '103.3333334' to each side of the equation. -103.3333334 + 103.3333334 + x = -103.355911571 + 103.3333334 Combine like terms: -103.3333334 + 103.3333334 = 0.0000000 0.0000000 + x = -103.355911571 + 103.3333334 x = -103.355911571 + 103.3333334 Combine like terms: -103.355911571 + 103.3333334 = -0.022578171 x = -0.022578171 Simplifying x = -0.022578171Solution
The solution to the problem is based on the solutions from the subproblems. x = {206.689244971, -0.022578171}
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