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Simplifying -9.8x2 + 40x + 30 = 0 Reorder the terms: 30 + 40x + -9.8x2 = 0 Solving 30 + 40x + -9.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9.8 the coefficient of the squared term: Divide each side by '-9.8'. -3.06122449 + -4.081632653x + x2 = 0 Move the constant term to the right: Add '3.06122449' to each side of the equation. -3.06122449 + -4.081632653x + 3.06122449 + x2 = 0 + 3.06122449 Reorder the terms: -3.06122449 + 3.06122449 + -4.081632653x + x2 = 0 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + -4.081632653x + x2 = 0 + 3.06122449 -4.081632653x + x2 = 0 + 3.06122449 Combine like terms: 0 + 3.06122449 = 3.06122449 -4.081632653x + x2 = 3.06122449 The x term is -4.081632653x. Take half its coefficient (-2.040816327). Square it (4.164931281) and add it to both sides. Add '4.164931281' to each side of the equation. -4.081632653x + 4.164931281 + x2 = 3.06122449 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653x + x2 = 3.06122449 + 4.164931281 Combine like terms: 3.06122449 + 4.164931281 = 7.226155771 4.164931281 + -4.081632653x + x2 = 7.226155771 Factor a perfect square on the left side: (x + -2.040816327)(x + -2.040816327) = 7.226155771 Calculate the square root of the right side: 2.688150995 Break this problem into two subproblems by setting (x + -2.040816327) equal to 2.688150995 and -2.688150995.Subproblem 1
x + -2.040816327 = 2.688150995 Simplifying x + -2.040816327 = 2.688150995 Reorder the terms: -2.040816327 + x = 2.688150995 Solving -2.040816327 + x = 2.688150995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + x = 2.688150995 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = 2.688150995 + 2.040816327 x = 2.688150995 + 2.040816327 Combine like terms: 2.688150995 + 2.040816327 = 4.728967322 x = 4.728967322 Simplifying x = 4.728967322Subproblem 2
x + -2.040816327 = -2.688150995 Simplifying x + -2.040816327 = -2.688150995 Reorder the terms: -2.040816327 + x = -2.688150995 Solving -2.040816327 + x = -2.688150995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + x = -2.688150995 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = -2.688150995 + 2.040816327 x = -2.688150995 + 2.040816327 Combine like terms: -2.688150995 + 2.040816327 = -0.647334668 x = -0.647334668 Simplifying x = -0.647334668Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.728967322, -0.647334668}
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