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Simplifying 4.9x2 + -40x + 80 = 0 Reorder the terms: 80 + -40x + 4.9x2 = 0 Solving 80 + -40x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 16.32653061 + -8.163265306x + x2 = 0 Move the constant term to the right: Add '-16.32653061' to each side of the equation. 16.32653061 + -8.163265306x + -16.32653061 + x2 = 0 + -16.32653061 Reorder the terms: 16.32653061 + -16.32653061 + -8.163265306x + x2 = 0 + -16.32653061 Combine like terms: 16.32653061 + -16.32653061 = 0.00000000 0.00000000 + -8.163265306x + x2 = 0 + -16.32653061 -8.163265306x + x2 = 0 + -16.32653061 Combine like terms: 0 + -16.32653061 = -16.32653061 -8.163265306x + x2 = -16.32653061 The x term is -8.163265306x. Take half its coefficient (-4.081632653). Square it (16.65972511) and add it to both sides. Add '16.65972511' to each side of the equation. -8.163265306x + 16.65972511 + x2 = -16.32653061 + 16.65972511 Reorder the terms: 16.65972511 + -8.163265306x + x2 = -16.32653061 + 16.65972511 Combine like terms: -16.32653061 + 16.65972511 = 0.3331945 16.65972511 + -8.163265306x + x2 = 0.3331945 Factor a perfect square on the left side: (x + -4.081632653)(x + -4.081632653) = 0.3331945 Calculate the square root of the right side: 0.577230023 Break this problem into two subproblems by setting (x + -4.081632653) equal to 0.577230023 and -0.577230023.Subproblem 1
x + -4.081632653 = 0.577230023 Simplifying x + -4.081632653 = 0.577230023 Reorder the terms: -4.081632653 + x = 0.577230023 Solving -4.081632653 + x = 0.577230023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + x = 0.577230023 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + x = 0.577230023 + 4.081632653 x = 0.577230023 + 4.081632653 Combine like terms: 0.577230023 + 4.081632653 = 4.658862676 x = 4.658862676 Simplifying x = 4.658862676Subproblem 2
x + -4.081632653 = -0.577230023 Simplifying x + -4.081632653 = -0.577230023 Reorder the terms: -4.081632653 + x = -0.577230023 Solving -4.081632653 + x = -0.577230023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + x = -0.577230023 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + x = -0.577230023 + 4.081632653 x = -0.577230023 + 4.081632653 Combine like terms: -0.577230023 + 4.081632653 = 3.50440263 x = 3.50440263 Simplifying x = 3.50440263Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.658862676, 3.50440263}
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