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Simplifying 4 = 0.08x2 + 1.6x + -16 Reorder the terms: 4 = -16 + 1.6x + 0.08x2 Solving 4 = -16 + 1.6x + 0.08x2 Solving for variable 'x'. Combine like terms: 4 + 16 = 20 20 + -1.6x + -0.08x2 = -16 + 1.6x + 0.08x2 + 16 + -1.6x + -0.08x2 Reorder the terms: 20 + -1.6x + -0.08x2 = -16 + 16 + 1.6x + -1.6x + 0.08x2 + -0.08x2 Combine like terms: -16 + 16 = 0 20 + -1.6x + -0.08x2 = 0 + 1.6x + -1.6x + 0.08x2 + -0.08x2 20 + -1.6x + -0.08x2 = 1.6x + -1.6x + 0.08x2 + -0.08x2 Combine like terms: 1.6x + -1.6x = 0.0 20 + -1.6x + -0.08x2 = 0.0 + 0.08x2 + -0.08x2 20 + -1.6x + -0.08x2 = 0.08x2 + -0.08x2 Combine like terms: 0.08x2 + -0.08x2 = 0.00 20 + -1.6x + -0.08x2 = 0.00 Begin completing the square. Divide all terms by -0.08 the coefficient of the squared term: Divide each side by '-0.08'. -250 + 20x + x2 = 0 Move the constant term to the right: Add '250' to each side of the equation. -250 + 20x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 20x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 20x + x2 = 0 + 250 20x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 20x + x2 = 250 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 = 250 + 100 Reorder the terms: 100 + 20x + x2 = 250 + 100 Combine like terms: 250 + 100 = 350 100 + 20x + x2 = 350 Factor a perfect square on the left side: (x + 10)(x + 10) = 350 Calculate the square root of the right side: 18.708286934 Break this problem into two subproblems by setting (x + 10) equal to 18.708286934 and -18.708286934.Subproblem 1
x + 10 = 18.708286934 Simplifying x + 10 = 18.708286934 Reorder the terms: 10 + x = 18.708286934 Solving 10 + x = 18.708286934 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 = 18.708286934 + -10 Combine like terms: 10 + -10 = 0 0 + x = 18.708286934 + -10 x = 18.708286934 + -10 Combine like terms: 18.708286934 + -10 = 8.708286934 x = 8.708286934 Simplifying x = 8.708286934Subproblem 2
x + 10 = -18.708286934 Simplifying x + 10 = -18.708286934 Reorder the terms: 10 + x = -18.708286934 Solving 10 + x = -18.708286934 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 = -18.708286934 + -10 Combine like terms: 10 + -10 = 0 0 + x = -18.708286934 + -10 x = -18.708286934 + -10 Combine like terms: -18.708286934 + -10 = -28.708286934 x = -28.708286934 Simplifying x = -28.708286934Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.708286934, -28.708286934}
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