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Simplifying 0 = x2 + -30x + 8 Reorder the terms: 0 = 8 + -30x + x2 Solving 0 = 8 + -30x + x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + 30x + -1x2 = 8 + -30x + x2 + -8 + 30x + -1x2 Reorder the terms: -8 + 30x + -1x2 = 8 + -8 + -30x + 30x + x2 + -1x2 Combine like terms: 8 + -8 = 0 -8 + 30x + -1x2 = 0 + -30x + 30x + x2 + -1x2 -8 + 30x + -1x2 = -30x + 30x + x2 + -1x2 Combine like terms: -30x + 30x = 0 -8 + 30x + -1x2 = 0 + x2 + -1x2 -8 + 30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8 + 30x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -30x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -30x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -30x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -30x + x2 = 0 + -8 -30x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -30x + x2 = -8 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -8 + 225 Reorder the terms: 225 + -30x + x2 = -8 + 225 Combine like terms: -8 + 225 = 217 225 + -30x + x2 = 217 Factor a perfect square on the left side: (x + -15)(x + -15) = 217 Calculate the square root of the right side: 14.730919863 Break this problem into two subproblems by setting (x + -15) equal to 14.730919863 and -14.730919863.Subproblem 1
x + -15 = 14.730919863 Simplifying x + -15 = 14.730919863 Reorder the terms: -15 + x = 14.730919863 Solving -15 + x = 14.730919863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 14.730919863 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.730919863 + 15 x = 14.730919863 + 15 Combine like terms: 14.730919863 + 15 = 29.730919863 x = 29.730919863 Simplifying x = 29.730919863Subproblem 2
x + -15 = -14.730919863 Simplifying x + -15 = -14.730919863 Reorder the terms: -15 + x = -14.730919863 Solving -15 + x = -14.730919863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -14.730919863 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.730919863 + 15 x = -14.730919863 + 15 Combine like terms: -14.730919863 + 15 = 0.269080137 x = 0.269080137 Simplifying x = 0.269080137Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.730919863, 0.269080137}
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