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Simplifying 3x2 + -78x + 500 = 0 Reorder the terms: 500 + -78x + 3x2 = 0 Solving 500 + -78x + 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'. 166.6666667 + -26x + x2 = 0 Move the constant term to the right: Add '-166.6666667' to each side of the equation. 166.6666667 + -26x + -166.6666667 + x2 = 0 + -166.6666667 Reorder the terms: 166.6666667 + -166.6666667 + -26x + x2 = 0 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + -26x + x2 = 0 + -166.6666667 -26x + x2 = 0 + -166.6666667 Combine like terms: 0 + -166.6666667 = -166.6666667 -26x + x2 = -166.6666667 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -166.6666667 + 169 Reorder the terms: 169 + -26x + x2 = -166.6666667 + 169 Combine like terms: -166.6666667 + 169 = 2.3333333 169 + -26x + x2 = 2.3333333 Factor a perfect square on the left side: (x + -13)(x + -13) = 2.3333333 Calculate the square root of the right side: 1.527525221 Break this problem into two subproblems by setting (x + -13) equal to 1.527525221 and -1.527525221.Subproblem 1
x + -13 = 1.527525221 Simplifying x + -13 = 1.527525221 Reorder the terms: -13 + x = 1.527525221 Solving -13 + x = 1.527525221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 1.527525221 + 13 Combine like terms: -13 + 13 = 0 0 + x = 1.527525221 + 13 x = 1.527525221 + 13 Combine like terms: 1.527525221 + 13 = 14.527525221 x = 14.527525221 Simplifying x = 14.527525221Subproblem 2
x + -13 = -1.527525221 Simplifying x + -13 = -1.527525221 Reorder the terms: -13 + x = -1.527525221 Solving -13 + x = -1.527525221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -1.527525221 + 13 Combine like terms: -13 + 13 = 0 0 + x = -1.527525221 + 13 x = -1.527525221 + 13 Combine like terms: -1.527525221 + 13 = 11.472474779 x = 11.472474779 Simplifying x = 11.472474779Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.527525221, 11.472474779}
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