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Simplifying 0.01(8x2 + -2x + 180) = 3.7 Reorder the terms: 0.01(180 + -2x + 8x2) = 3.7 (180 * 0.01 + -2x * 0.01 + 8x2 * 0.01) = 3.7 (1.8 + -0.02x + 0.08x2) = 3.7 Solving 1.8 + -0.02x + 0.08x2 = 3.7 Solving for variable 'x'. Reorder the terms: 1.8 + -3.7 + -0.02x + 0.08x2 = 3.7 + -3.7 Combine like terms: 1.8 + -3.7 = -1.9 -1.9 + -0.02x + 0.08x2 = 3.7 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 -1.9 + -0.02x + 0.08x2 = 0.0 Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. -23.75 + -0.25x + x2 = 0 Move the constant term to the right: Add '23.75' to each side of the equation. -23.75 + -0.25x + 23.75 + x2 = 0 + 23.75 Reorder the terms: -23.75 + 23.75 + -0.25x + x2 = 0 + 23.75 Combine like terms: -23.75 + 23.75 = 0.00 0.00 + -0.25x + x2 = 0 + 23.75 -0.25x + x2 = 0 + 23.75 Combine like terms: 0 + 23.75 = 23.75 -0.25x + x2 = 23.75 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 23.75 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 23.75 + 0.015625 Combine like terms: 23.75 + 0.015625 = 23.765625 0.015625 + -0.25x + x2 = 23.765625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 23.765625 Calculate the square root of the right side: 4.875 Break this problem into two subproblems by setting (x + -0.125) equal to 4.875 and -4.875.Subproblem 1
x + -0.125 = 4.875 Simplifying x + -0.125 = 4.875 Reorder the terms: -0.125 + x = 4.875 Solving -0.125 + x = 4.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 4.875 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 4.875 + 0.125 x = 4.875 + 0.125 Combine like terms: 4.875 + 0.125 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -0.125 = -4.875 Simplifying x + -0.125 = -4.875 Reorder the terms: -0.125 + x = -4.875 Solving -0.125 + x = -4.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -4.875 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -4.875 + 0.125 x = -4.875 + 0.125 Combine like terms: -4.875 + 0.125 = -4.75 x = -4.75 Simplifying x = -4.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, -4.75}
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