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Simplifying 17.2x2 + 1.58x + -0.2025 = 0 Reorder the terms: -0.2025 + 1.58x + 17.2x2 = 0 Solving -0.2025 + 1.58x + 17.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17.2 the coefficient of the squared term: Divide each side by '17.2'. -0.01177325581 + 0.09186046512x + x2 = 0 Move the constant term to the right: Add '0.01177325581' to each side of the equation. -0.01177325581 + 0.09186046512x + 0.01177325581 + x2 = 0 + 0.01177325581 Reorder the terms: -0.01177325581 + 0.01177325581 + 0.09186046512x + x2 = 0 + 0.01177325581 Combine like terms: -0.01177325581 + 0.01177325581 = 0.00000000000 0.00000000000 + 0.09186046512x + x2 = 0 + 0.01177325581 0.09186046512x + x2 = 0 + 0.01177325581 Combine like terms: 0 + 0.01177325581 = 0.01177325581 0.09186046512x + x2 = 0.01177325581 The x term is 0.09186046512x. Take half its coefficient (0.04593023256). Square it (0.002109586263) and add it to both sides. Add '0.002109586263' to each side of the equation. 0.09186046512x + 0.002109586263 + x2 = 0.01177325581 + 0.002109586263 Reorder the terms: 0.002109586263 + 0.09186046512x + x2 = 0.01177325581 + 0.002109586263 Combine like terms: 0.01177325581 + 0.002109586263 = 0.013882842073 0.002109586263 + 0.09186046512x + x2 = 0.013882842073 Factor a perfect square on the left side: (x + 0.04593023256)(x + 0.04593023256) = 0.013882842073 Calculate the square root of the right side: 0.117825473 Break this problem into two subproblems by setting (x + 0.04593023256) equal to 0.117825473 and -0.117825473.Subproblem 1
x + 0.04593023256 = 0.117825473 Simplifying x + 0.04593023256 = 0.117825473 Reorder the terms: 0.04593023256 + x = 0.117825473 Solving 0.04593023256 + x = 0.117825473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04593023256' to each side of the equation. 0.04593023256 + -0.04593023256 + x = 0.117825473 + -0.04593023256 Combine like terms: 0.04593023256 + -0.04593023256 = 0.00000000000 0.00000000000 + x = 0.117825473 + -0.04593023256 x = 0.117825473 + -0.04593023256 Combine like terms: 0.117825473 + -0.04593023256 = 0.07189524044 x = 0.07189524044 Simplifying x = 0.07189524044Subproblem 2
x + 0.04593023256 = -0.117825473 Simplifying x + 0.04593023256 = -0.117825473 Reorder the terms: 0.04593023256 + x = -0.117825473 Solving 0.04593023256 + x = -0.117825473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04593023256' to each side of the equation. 0.04593023256 + -0.04593023256 + x = -0.117825473 + -0.04593023256 Combine like terms: 0.04593023256 + -0.04593023256 = 0.00000000000 0.00000000000 + x = -0.117825473 + -0.04593023256 x = -0.117825473 + -0.04593023256 Combine like terms: -0.117825473 + -0.04593023256 = -0.16375570556 x = -0.16375570556 Simplifying x = -0.16375570556Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.07189524044, -0.16375570556}
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