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Simplifying -0.06x2 + 1.2x + 28 = 0 Reorder the terms: 28 + 1.2x + -0.06x2 = 0 Solving 28 + 1.2x + -0.06x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.06 the coefficient of the squared term: Divide each side by '-0.06'. -466.6666667 + -20x + x2 = 0 Move the constant term to the right: Add '466.6666667' to each side of the equation. -466.6666667 + -20x + 466.6666667 + x2 = 0 + 466.6666667 Reorder the terms: -466.6666667 + 466.6666667 + -20x + x2 = 0 + 466.6666667 Combine like terms: -466.6666667 + 466.6666667 = 0.0000000 0.0000000 + -20x + x2 = 0 + 466.6666667 -20x + x2 = 0 + 466.6666667 Combine like terms: 0 + 466.6666667 = 466.6666667 -20x + x2 = 466.6666667 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 = 466.6666667 + 100 Reorder the terms: 100 + -20x + x2 = 466.6666667 + 100 Combine like terms: 466.6666667 + 100 = 566.6666667 100 + -20x + x2 = 566.6666667 Factor a perfect square on the left side: (x + -10)(x + -10) = 566.6666667 Calculate the square root of the right side: 23.804761429 Break this problem into two subproblems by setting (x + -10) equal to 23.804761429 and -23.804761429.Subproblem 1
x + -10 = 23.804761429 Simplifying x + -10 = 23.804761429 Reorder the terms: -10 + x = 23.804761429 Solving -10 + x = 23.804761429 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 = 23.804761429 + 10 Combine like terms: -10 + 10 = 0 0 + x = 23.804761429 + 10 x = 23.804761429 + 10 Combine like terms: 23.804761429 + 10 = 33.804761429 x = 33.804761429 Simplifying x = 33.804761429Subproblem 2
x + -10 = -23.804761429 Simplifying x + -10 = -23.804761429 Reorder the terms: -10 + x = -23.804761429 Solving -10 + x = -23.804761429 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 = -23.804761429 + 10 Combine like terms: -10 + 10 = 0 0 + x = -23.804761429 + 10 x = -23.804761429 + 10 Combine like terms: -23.804761429 + 10 = -13.804761429 x = -13.804761429 Simplifying x = -13.804761429Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.804761429, -13.804761429}
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