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Simplifying -4.9x2 + 9.8x + 0 = -2 Reorder the terms: 0 + 9.8x + -4.9x2 = -2 Remove the zero: 9.8x + -4.9x2 = -2 Solving 9.8x + -4.9x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 9.8x + -4.9x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 9.8x + -4.9x2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.4081632653 + -2x + x2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -2x + 0.4081632653 + x2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -2x + x2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + 0.4081632653 -2x + x2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -2x + x2 = 0.4081632653 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.4081632653 + 1 Reorder the terms: 1 + -2x + x2 = 0.4081632653 + 1 Combine like terms: 0.4081632653 + 1 = 1.4081632653 1 + -2x + x2 = 1.4081632653 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.4081632653 Calculate the square root of the right side: 1.186660552 Break this problem into two subproblems by setting (x + -1) equal to 1.186660552 and -1.186660552.Subproblem 1
x + -1 = 1.186660552 Simplifying x + -1 = 1.186660552 Reorder the terms: -1 + x = 1.186660552 Solving -1 + x = 1.186660552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.186660552 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.186660552 + 1 x = 1.186660552 + 1 Combine like terms: 1.186660552 + 1 = 2.186660552 x = 2.186660552 Simplifying x = 2.186660552Subproblem 2
x + -1 = -1.186660552 Simplifying x + -1 = -1.186660552 Reorder the terms: -1 + x = -1.186660552 Solving -1 + x = -1.186660552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.186660552 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.186660552 + 1 x = -1.186660552 + 1 Combine like terms: -1.186660552 + 1 = -0.186660552 x = -0.186660552 Simplifying x = -0.186660552Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.186660552, -0.186660552}
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