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Simplifying 0 = 5x2 + -30x + 31 Reorder the terms: 0 = 31 + -30x + 5x2 Solving 0 = 31 + -30x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -31 = -31 -31 + 30x + -5x2 = 31 + -30x + 5x2 + -31 + 30x + -5x2 Reorder the terms: -31 + 30x + -5x2 = 31 + -31 + -30x + 30x + 5x2 + -5x2 Combine like terms: 31 + -31 = 0 -31 + 30x + -5x2 = 0 + -30x + 30x + 5x2 + -5x2 -31 + 30x + -5x2 = -30x + 30x + 5x2 + -5x2 Combine like terms: -30x + 30x = 0 -31 + 30x + -5x2 = 0 + 5x2 + -5x2 -31 + 30x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -31 + 30x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 6.2 + -6x + x2 = 0 Move the constant term to the right: Add '-6.2' to each side of the equation. 6.2 + -6x + -6.2 + x2 = 0 + -6.2 Reorder the terms: 6.2 + -6.2 + -6x + x2 = 0 + -6.2 Combine like terms: 6.2 + -6.2 = 0.0 0.0 + -6x + x2 = 0 + -6.2 -6x + x2 = 0 + -6.2 Combine like terms: 0 + -6.2 = -6.2 -6x + x2 = -6.2 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -6.2 + 9 Reorder the terms: 9 + -6x + x2 = -6.2 + 9 Combine like terms: -6.2 + 9 = 2.8 9 + -6x + x2 = 2.8 Factor a perfect square on the left side: (x + -3)(x + -3) = 2.8 Calculate the square root of the right side: 1.673320053 Break this problem into two subproblems by setting (x + -3) equal to 1.673320053 and -1.673320053.Subproblem 1
x + -3 = 1.673320053 Simplifying x + -3 = 1.673320053 Reorder the terms: -3 + x = 1.673320053 Solving -3 + x = 1.673320053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.673320053 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.673320053 + 3 x = 1.673320053 + 3 Combine like terms: 1.673320053 + 3 = 4.673320053 x = 4.673320053 Simplifying x = 4.673320053Subproblem 2
x + -3 = -1.673320053 Simplifying x + -3 = -1.673320053 Reorder the terms: -3 + x = -1.673320053 Solving -3 + x = -1.673320053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.673320053 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.673320053 + 3 x = -1.673320053 + 3 Combine like terms: -1.673320053 + 3 = 1.326679947 x = 1.326679947 Simplifying x = 1.326679947Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.673320053, 1.326679947}
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