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Simplifying -0.008x2 + 0.103x + -0.195 = 0 Reorder the terms: -0.195 + 0.103x + -0.008x2 = 0 Solving -0.195 + 0.103x + -0.008x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.008 the coefficient of the squared term: Divide each side by '-0.008'. 24.375 + -12.875x + x2 = 0 Move the constant term to the right: Add '-24.375' to each side of the equation. 24.375 + -12.875x + -24.375 + x2 = 0 + -24.375 Reorder the terms: 24.375 + -24.375 + -12.875x + x2 = 0 + -24.375 Combine like terms: 24.375 + -24.375 = 0.000 0.000 + -12.875x + x2 = 0 + -24.375 -12.875x + x2 = 0 + -24.375 Combine like terms: 0 + -24.375 = -24.375 -12.875x + x2 = -24.375 The x term is -12.875x. Take half its coefficient (-6.4375). Square it (41.44140625) and add it to both sides. Add '41.44140625' to each side of the equation. -12.875x + 41.44140625 + x2 = -24.375 + 41.44140625 Reorder the terms: 41.44140625 + -12.875x + x2 = -24.375 + 41.44140625 Combine like terms: -24.375 + 41.44140625 = 17.06640625 41.44140625 + -12.875x + x2 = 17.06640625 Factor a perfect square on the left side: (x + -6.4375)(x + -6.4375) = 17.06640625 Calculate the square root of the right side: 4.131150717 Break this problem into two subproblems by setting (x + -6.4375) equal to 4.131150717 and -4.131150717.Subproblem 1
x + -6.4375 = 4.131150717 Simplifying x + -6.4375 = 4.131150717 Reorder the terms: -6.4375 + x = 4.131150717 Solving -6.4375 + x = 4.131150717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.4375' to each side of the equation. -6.4375 + 6.4375 + x = 4.131150717 + 6.4375 Combine like terms: -6.4375 + 6.4375 = 0.0000 0.0000 + x = 4.131150717 + 6.4375 x = 4.131150717 + 6.4375 Combine like terms: 4.131150717 + 6.4375 = 10.568650717 x = 10.568650717 Simplifying x = 10.568650717Subproblem 2
x + -6.4375 = -4.131150717 Simplifying x + -6.4375 = -4.131150717 Reorder the terms: -6.4375 + x = -4.131150717 Solving -6.4375 + x = -4.131150717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.4375' to each side of the equation. -6.4375 + 6.4375 + x = -4.131150717 + 6.4375 Combine like terms: -6.4375 + 6.4375 = 0.0000 0.0000 + x = -4.131150717 + 6.4375 x = -4.131150717 + 6.4375 Combine like terms: -4.131150717 + 6.4375 = 2.306349283 x = 2.306349283 Simplifying x = 2.306349283Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.568650717, 2.306349283}
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