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Simplifying 3x2 + -30x = 8 Reorder the terms: -30x + 3x2 = 8 Solving -30x + 3x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -30x + 3x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + -10x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -10x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -10x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -10x + x2 = 0 + 2.666666667 -10x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -10x + x2 = 2.666666667 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 = 2.666666667 + 25 Reorder the terms: 25 + -10x + x2 = 2.666666667 + 25 Combine like terms: 2.666666667 + 25 = 27.666666667 25 + -10x + x2 = 27.666666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 27.666666667 Calculate the square root of the right side: 5.259911279 Break this problem into two subproblems by setting (x + -5) equal to 5.259911279 and -5.259911279.Subproblem 1
x + -5 = 5.259911279 Simplifying x + -5 = 5.259911279 Reorder the terms: -5 + x = 5.259911279 Solving -5 + x = 5.259911279 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 = 5.259911279 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.259911279 + 5 x = 5.259911279 + 5 Combine like terms: 5.259911279 + 5 = 10.259911279 x = 10.259911279 Simplifying x = 10.259911279Subproblem 2
x + -5 = -5.259911279 Simplifying x + -5 = -5.259911279 Reorder the terms: -5 + x = -5.259911279 Solving -5 + x = -5.259911279 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 = -5.259911279 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.259911279 + 5 x = -5.259911279 + 5 Combine like terms: -5.259911279 + 5 = -0.259911279 x = -0.259911279 Simplifying x = -0.259911279Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.259911279, -0.259911279}
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