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Simplifying 3x2 + 80x + 300 = 0 Reorder the terms: 300 + 80x + 3x2 = 0 Solving 300 + 80x + 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'. 100 + 26.66666667x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + 26.66666667x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + 26.66666667x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 26.66666667x + x2 = 0 + -100 26.66666667x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 26.66666667x + x2 = -100 The x term is 26.66666667x. Take half its coefficient (13.33333334). Square it (177.7777780) and add it to both sides. Add '177.7777780' to each side of the equation. 26.66666667x + 177.7777780 + x2 = -100 + 177.7777780 Reorder the terms: 177.7777780 + 26.66666667x + x2 = -100 + 177.7777780 Combine like terms: -100 + 177.7777780 = 77.777778 177.7777780 + 26.66666667x + x2 = 77.777778 Factor a perfect square on the left side: (x + 13.33333334)(x + 13.33333334) = 77.777778 Calculate the square root of the right side: 8.819171049 Break this problem into two subproblems by setting (x + 13.33333334) equal to 8.819171049 and -8.819171049.Subproblem 1
x + 13.33333334 = 8.819171049 Simplifying x + 13.33333334 = 8.819171049 Reorder the terms: 13.33333334 + x = 8.819171049 Solving 13.33333334 + x = 8.819171049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.33333334' to each side of the equation. 13.33333334 + -13.33333334 + x = 8.819171049 + -13.33333334 Combine like terms: 13.33333334 + -13.33333334 = 0.00000000 0.00000000 + x = 8.819171049 + -13.33333334 x = 8.819171049 + -13.33333334 Combine like terms: 8.819171049 + -13.33333334 = -4.514162291 x = -4.514162291 Simplifying x = -4.514162291Subproblem 2
x + 13.33333334 = -8.819171049 Simplifying x + 13.33333334 = -8.819171049 Reorder the terms: 13.33333334 + x = -8.819171049 Solving 13.33333334 + x = -8.819171049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.33333334' to each side of the equation. 13.33333334 + -13.33333334 + x = -8.819171049 + -13.33333334 Combine like terms: 13.33333334 + -13.33333334 = 0.00000000 0.00000000 + x = -8.819171049 + -13.33333334 x = -8.819171049 + -13.33333334 Combine like terms: -8.819171049 + -13.33333334 = -22.152504389 x = -22.152504389 Simplifying x = -22.152504389Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.514162291, -22.152504389}
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