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Simplifying 20 = -4.9x2 + 20x Reorder the terms: 20 = 20x + -4.9x2 Solving 20 = 20x + -4.9x2 Solving for variable 'x'. Reorder the terms: 20 + -20x + 4.9x2 = 20x + -20x + -4.9x2 + 4.9x2 Combine like terms: 20x + -20x = 0 20 + -20x + 4.9x2 = 0 + -4.9x2 + 4.9x2 20 + -20x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 20 + -20x + 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'. 4.081632653 + -4.081632653x + x2 = 0 Move the constant term to the right: Add '-4.081632653' to each side of the equation. 4.081632653 + -4.081632653x + -4.081632653 + x2 = 0 + -4.081632653 Reorder the terms: 4.081632653 + -4.081632653 + -4.081632653x + x2 = 0 + -4.081632653 Combine like terms: 4.081632653 + -4.081632653 = 0.000000000 0.000000000 + -4.081632653x + x2 = 0 + -4.081632653 -4.081632653x + x2 = 0 + -4.081632653 Combine like terms: 0 + -4.081632653 = -4.081632653 -4.081632653x + x2 = -4.081632653 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 = -4.081632653 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653x + x2 = -4.081632653 + 4.164931281 Combine like terms: -4.081632653 + 4.164931281 = 0.083298628 4.164931281 + -4.081632653x + x2 = 0.083298628 Factor a perfect square on the left side: (x + -2.040816327)(x + -2.040816327) = 0.083298628 Calculate the square root of the right side: 0.288615017 Break this problem into two subproblems by setting (x + -2.040816327) equal to 0.288615017 and -0.288615017.Subproblem 1
x + -2.040816327 = 0.288615017 Simplifying x + -2.040816327 = 0.288615017 Reorder the terms: -2.040816327 + x = 0.288615017 Solving -2.040816327 + x = 0.288615017 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 = 0.288615017 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = 0.288615017 + 2.040816327 x = 0.288615017 + 2.040816327 Combine like terms: 0.288615017 + 2.040816327 = 2.329431344 x = 2.329431344 Simplifying x = 2.329431344Subproblem 2
x + -2.040816327 = -0.288615017 Simplifying x + -2.040816327 = -0.288615017 Reorder the terms: -2.040816327 + x = -0.288615017 Solving -2.040816327 + x = -0.288615017 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 = -0.288615017 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = -0.288615017 + 2.040816327 x = -0.288615017 + 2.040816327 Combine like terms: -0.288615017 + 2.040816327 = 1.75220131 x = 1.75220131 Simplifying x = 1.75220131Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.329431344, 1.75220131}
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