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Simplifying -4.9x2 + 4.9x + 0.8 = 0 Reorder the terms: 0.8 + 4.9x + -4.9x2 = 0 Solving 0.8 + 4.9x + -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'. -0.1632653061 + -1x + x2 = 0 Move the constant term to the right: Add '0.1632653061' to each side of the equation. -0.1632653061 + -1x + 0.1632653061 + x2 = 0 + 0.1632653061 Reorder the terms: -0.1632653061 + 0.1632653061 + -1x + x2 = 0 + 0.1632653061 Combine like terms: -0.1632653061 + 0.1632653061 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.1632653061 -1x + x2 = 0 + 0.1632653061 Combine like terms: 0 + 0.1632653061 = 0.1632653061 -1x + x2 = 0.1632653061 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.1632653061 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.1632653061 + 0.25 Combine like terms: 0.1632653061 + 0.25 = 0.4132653061 0.25 + -1x + x2 = 0.4132653061 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.4132653061 Calculate the square root of the right side: 0.642857143 Break this problem into two subproblems by setting (x + -0.5) equal to 0.642857143 and -0.642857143.Subproblem 1
x + -0.5 = 0.642857143 Simplifying x + -0.5 = 0.642857143 Reorder the terms: -0.5 + x = 0.642857143 Solving -0.5 + x = 0.642857143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.642857143 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.642857143 + 0.5 x = 0.642857143 + 0.5 Combine like terms: 0.642857143 + 0.5 = 1.142857143 x = 1.142857143 Simplifying x = 1.142857143Subproblem 2
x + -0.5 = -0.642857143 Simplifying x + -0.5 = -0.642857143 Reorder the terms: -0.5 + x = -0.642857143 Solving -0.5 + x = -0.642857143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.642857143 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.642857143 + 0.5 x = -0.642857143 + 0.5 Combine like terms: -0.642857143 + 0.5 = -0.142857143 x = -0.142857143 Simplifying x = -0.142857143Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.142857143, -0.142857143}
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