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Simplifying 0.197x2 + 0.087x + -0.473 = 0 Reorder the terms: -0.473 + 0.087x + 0.197x2 = 0 Solving -0.473 + 0.087x + 0.197x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.197 the coefficient of the squared term: Divide each side by '0.197'. -2.401015228 + 0.4416243655x + x2 = 0 Move the constant term to the right: Add '2.401015228' to each side of the equation. -2.401015228 + 0.4416243655x + 2.401015228 + x2 = 0 + 2.401015228 Reorder the terms: -2.401015228 + 2.401015228 + 0.4416243655x + x2 = 0 + 2.401015228 Combine like terms: -2.401015228 + 2.401015228 = 0.000000000 0.000000000 + 0.4416243655x + x2 = 0 + 2.401015228 0.4416243655x + x2 = 0 + 2.401015228 Combine like terms: 0 + 2.401015228 = 2.401015228 0.4416243655x + x2 = 2.401015228 The x term is 0.4416243655x. Take half its coefficient (0.2208121828). Square it (0.04875802007) and add it to both sides. Add '0.04875802007' to each side of the equation. 0.4416243655x + 0.04875802007 + x2 = 2.401015228 + 0.04875802007 Reorder the terms: 0.04875802007 + 0.4416243655x + x2 = 2.401015228 + 0.04875802007 Combine like terms: 2.401015228 + 0.04875802007 = 2.44977324807 0.04875802007 + 0.4416243655x + x2 = 2.44977324807 Factor a perfect square on the left side: (x + 0.2208121828)(x + 0.2208121828) = 2.44977324807 Calculate the square root of the right side: 1.565175149 Break this problem into two subproblems by setting (x + 0.2208121828) equal to 1.565175149 and -1.565175149.Subproblem 1
x + 0.2208121828 = 1.565175149 Simplifying x + 0.2208121828 = 1.565175149 Reorder the terms: 0.2208121828 + x = 1.565175149 Solving 0.2208121828 + x = 1.565175149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2208121828' to each side of the equation. 0.2208121828 + -0.2208121828 + x = 1.565175149 + -0.2208121828 Combine like terms: 0.2208121828 + -0.2208121828 = 0.0000000000 0.0000000000 + x = 1.565175149 + -0.2208121828 x = 1.565175149 + -0.2208121828 Combine like terms: 1.565175149 + -0.2208121828 = 1.3443629662 x = 1.3443629662 Simplifying x = 1.3443629662Subproblem 2
x + 0.2208121828 = -1.565175149 Simplifying x + 0.2208121828 = -1.565175149 Reorder the terms: 0.2208121828 + x = -1.565175149 Solving 0.2208121828 + x = -1.565175149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2208121828' to each side of the equation. 0.2208121828 + -0.2208121828 + x = -1.565175149 + -0.2208121828 Combine like terms: 0.2208121828 + -0.2208121828 = 0.0000000000 0.0000000000 + x = -1.565175149 + -0.2208121828 x = -1.565175149 + -0.2208121828 Combine like terms: -1.565175149 + -0.2208121828 = -1.7859873318 x = -1.7859873318 Simplifying x = -1.7859873318Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3443629662, -1.7859873318}
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