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Simplifying -4.9x2 + x + 35 = 0 Reorder the terms: 35 + x + -4.9x2 = 0 Solving 35 + x + -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'. -7.142857143 + -0.2040816327x + x2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + -0.2040816327x + 7.142857143 + x2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + -0.2040816327x + x2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + -0.2040816327x + x2 = 0 + 7.142857143 -0.2040816327x + x2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 -0.2040816327x + x2 = 7.142857143 The x term is x. 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. -0.2040816327x + 0.25 + x2 = 7.142857143 + 0.25 Reorder the terms: 0.25 + -0.2040816327x + x2 = 7.142857143 + 0.25 Combine like terms: 7.142857143 + 0.25 = 7.392857143 0.25 + -0.2040816327x + x2 = 7.392857143 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7.392857143 Calculate the square root of the right side: 2.718980902 Break this problem into two subproblems by setting (x + 0.5) equal to 2.718980902 and -2.718980902.Subproblem 1
x + 0.5 = 2.718980902 Simplifying x + 0.5 = 2.718980902 Reorder the terms: 0.5 + x = 2.718980902 Solving 0.5 + x = 2.718980902 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 = 2.718980902 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.718980902 + -0.5 x = 2.718980902 + -0.5 Combine like terms: 2.718980902 + -0.5 = 2.218980902 x = 2.218980902 Simplifying x = 2.218980902Subproblem 2
x + 0.5 = -2.718980902 Simplifying x + 0.5 = -2.718980902 Reorder the terms: 0.5 + x = -2.718980902 Solving 0.5 + x = -2.718980902 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 = -2.718980902 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.718980902 + -0.5 x = -2.718980902 + -0.5 Combine like terms: -2.718980902 + -0.5 = -3.218980902 x = -3.218980902 Simplifying x = -3.218980902Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.218980902, -3.218980902}
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