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Simplifying 3x2 + -30x + 68 = 0 Reorder the terms: 68 + -30x + 3x2 = 0 Solving 68 + -30x + 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'. 22.66666667 + -10x + x2 = 0 Move the constant term to the right: Add '-22.66666667' to each side of the equation. 22.66666667 + -10x + -22.66666667 + x2 = 0 + -22.66666667 Reorder the terms: 22.66666667 + -22.66666667 + -10x + x2 = 0 + -22.66666667 Combine like terms: 22.66666667 + -22.66666667 = 0.00000000 0.00000000 + -10x + x2 = 0 + -22.66666667 -10x + x2 = 0 + -22.66666667 Combine like terms: 0 + -22.66666667 = -22.66666667 -10x + x2 = -22.66666667 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -22.66666667 + 25 Reorder the terms: 25 + -10x + x2 = -22.66666667 + 25 Combine like terms: -22.66666667 + 25 = 2.33333333 25 + -10x + x2 = 2.33333333 Factor a perfect square on the left side: (x + -5)(x + -5) = 2.33333333 Calculate the square root of the right side: 1.527525231 Break this problem into two subproblems by setting (x + -5) equal to 1.527525231 and -1.527525231.Subproblem 1
x + -5 = 1.527525231 Simplifying x + -5 = 1.527525231 Reorder the terms: -5 + x = 1.527525231 Solving -5 + x = 1.527525231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 1.527525231 + 5 Combine like terms: -5 + 5 = 0 0 + x = 1.527525231 + 5 x = 1.527525231 + 5 Combine like terms: 1.527525231 + 5 = 6.527525231 x = 6.527525231 Simplifying x = 6.527525231Subproblem 2
x + -5 = -1.527525231 Simplifying x + -5 = -1.527525231 Reorder the terms: -5 + x = -1.527525231 Solving -5 + x = -1.527525231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -1.527525231 + 5 Combine like terms: -5 + 5 = 0 0 + x = -1.527525231 + 5 x = -1.527525231 + 5 Combine like terms: -1.527525231 + 5 = 3.472474769 x = 3.472474769 Simplifying x = 3.472474769Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.527525231, 3.472474769}
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