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Simplifying -4.9x2 + 6.86x + -0.3 = 0 Reorder the terms: -0.3 + 6.86x + -4.9x2 = 0 Solving -0.3 + 6.86x + -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'. 0.0612244898 + -1.4x + x2 = 0 Move the constant term to the right: Add '-0.0612244898' to each side of the equation. 0.0612244898 + -1.4x + -0.0612244898 + x2 = 0 + -0.0612244898 Reorder the terms: 0.0612244898 + -0.0612244898 + -1.4x + x2 = 0 + -0.0612244898 Combine like terms: 0.0612244898 + -0.0612244898 = 0.0000000000 0.0000000000 + -1.4x + x2 = 0 + -0.0612244898 -1.4x + x2 = 0 + -0.0612244898 Combine like terms: 0 + -0.0612244898 = -0.0612244898 -1.4x + x2 = -0.0612244898 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = -0.0612244898 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = -0.0612244898 + 0.49 Combine like terms: -0.0612244898 + 0.49 = 0.4287755102 0.49 + -1.4x + x2 = 0.4287755102 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.4287755102 Calculate the square root of the right side: 0.654809522 Break this problem into two subproblems by setting (x + -0.7) equal to 0.654809522 and -0.654809522.Subproblem 1
x + -0.7 = 0.654809522 Simplifying x + -0.7 = 0.654809522 Reorder the terms: -0.7 + x = 0.654809522 Solving -0.7 + x = 0.654809522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.654809522 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.654809522 + 0.7 x = 0.654809522 + 0.7 Combine like terms: 0.654809522 + 0.7 = 1.354809522 x = 1.354809522 Simplifying x = 1.354809522Subproblem 2
x + -0.7 = -0.654809522 Simplifying x + -0.7 = -0.654809522 Reorder the terms: -0.7 + x = -0.654809522 Solving -0.7 + x = -0.654809522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -0.654809522 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.654809522 + 0.7 x = -0.654809522 + 0.7 Combine like terms: -0.654809522 + 0.7 = 0.045190478 x = 0.045190478 Simplifying x = 0.045190478Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.354809522, 0.045190478}
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