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Simplifying -95 = 9x + -4.9x2 Solving -95 = 9x + -4.9x2 Solving for variable 'x'. Reorder the terms: -95 + -9x + 4.9x2 = 9x + -9x + -4.9x2 + 4.9x2 Combine like terms: 9x + -9x = 0 -95 + -9x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -95 + -9x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -95 + -9x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -19.3877551 + -1.836734694x + x2 = 0 Move the constant term to the right: Add '19.3877551' to each side of the equation. -19.3877551 + -1.836734694x + 19.3877551 + x2 = 0 + 19.3877551 Reorder the terms: -19.3877551 + 19.3877551 + -1.836734694x + x2 = 0 + 19.3877551 Combine like terms: -19.3877551 + 19.3877551 = 0.0000000 0.0000000 + -1.836734694x + x2 = 0 + 19.3877551 -1.836734694x + x2 = 0 + 19.3877551 Combine like terms: 0 + 19.3877551 = 19.3877551 -1.836734694x + x2 = 19.3877551 The x term is -1.836734694x. Take half its coefficient (-0.918367347). Square it (0.8433985840) and add it to both sides. Add '0.8433985840' to each side of the equation. -1.836734694x + 0.8433985840 + x2 = 19.3877551 + 0.8433985840 Reorder the terms: 0.8433985840 + -1.836734694x + x2 = 19.3877551 + 0.8433985840 Combine like terms: 19.3877551 + 0.8433985840 = 20.231153684 0.8433985840 + -1.836734694x + x2 = 20.231153684 Factor a perfect square on the left side: (x + -0.918367347)(x + -0.918367347) = 20.231153684 Calculate the square root of the right side: 4.497905477 Break this problem into two subproblems by setting (x + -0.918367347) equal to 4.497905477 and -4.497905477.Subproblem 1
x + -0.918367347 = 4.497905477 Simplifying x + -0.918367347 = 4.497905477 Reorder the terms: -0.918367347 + x = 4.497905477 Solving -0.918367347 + x = 4.497905477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = 4.497905477 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = 4.497905477 + 0.918367347 x = 4.497905477 + 0.918367347 Combine like terms: 4.497905477 + 0.918367347 = 5.416272824 x = 5.416272824 Simplifying x = 5.416272824Subproblem 2
x + -0.918367347 = -4.497905477 Simplifying x + -0.918367347 = -4.497905477 Reorder the terms: -0.918367347 + x = -4.497905477 Solving -0.918367347 + x = -4.497905477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = -4.497905477 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = -4.497905477 + 0.918367347 x = -4.497905477 + 0.918367347 Combine like terms: -4.497905477 + 0.918367347 = -3.57953813 x = -3.57953813 Simplifying x = -3.57953813Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.416272824, -3.57953813}
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