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Simplifying 0 = 0.3x2 + -6x + 30 Reorder the terms: 0 = 30 + -6x + 0.3x2 Solving 0 = 30 + -6x + 0.3x2 Solving for variable 'x'. Combine like terms: 0 + -30 = -30 -30 + 6x + -0.3x2 = 30 + -6x + 0.3x2 + -30 + 6x + -0.3x2 Reorder the terms: -30 + 6x + -0.3x2 = 30 + -30 + -6x + 6x + 0.3x2 + -0.3x2 Combine like terms: 30 + -30 = 0 -30 + 6x + -0.3x2 = 0 + -6x + 6x + 0.3x2 + -0.3x2 -30 + 6x + -0.3x2 = -6x + 6x + 0.3x2 + -0.3x2 Combine like terms: -6x + 6x = 0 -30 + 6x + -0.3x2 = 0 + 0.3x2 + -0.3x2 -30 + 6x + -0.3x2 = 0.3x2 + -0.3x2 Combine like terms: 0.3x2 + -0.3x2 = 0.0 -30 + 6x + -0.3x2 = 0.0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. 100 + -20x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -20x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -20x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -20x + x2 = 0 + -100 -20x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -20x + x2 = -100 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -100 + 100 Reorder the terms: 100 + -20x + x2 = -100 + 100 Combine like terms: -100 + 100 = 0 100 + -20x + x2 = 0 Factor a perfect square on the left side: (x + -10)(x + -10) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -10) equal to 0 and 0.Subproblem 1
x + -10 = 0 Simplifying x + -10 = 0 Reorder the terms: -10 + x = 0 Solving -10 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Simplifying x = 10Subproblem 2
x + -10 = 0 Simplifying x + -10 = 0 Reorder the terms: -10 + x = 0 Solving -10 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, 10}
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