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Simplifying 1.4x2 + -1x + -30 = 0 Reorder the terms: -30 + -1x + 1.4x2 = 0 Solving -30 + -1x + 1.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.4 the coefficient of the squared term: Divide each side by '1.4'. -21.42857143 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '21.42857143' to each side of the equation. -21.42857143 + -0.7142857143x + 21.42857143 + x2 = 0 + 21.42857143 Reorder the terms: -21.42857143 + 21.42857143 + -0.7142857143x + x2 = 0 + 21.42857143 Combine like terms: -21.42857143 + 21.42857143 = 0.00000000 0.00000000 + -0.7142857143x + x2 = 0 + 21.42857143 -0.7142857143x + x2 = 0 + 21.42857143 Combine like terms: 0 + 21.42857143 = 21.42857143 -0.7142857143x + x2 = 21.42857143 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 21.42857143 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 21.42857143 + 0.1275510204 Combine like terms: 21.42857143 + 0.1275510204 = 21.5561224504 0.1275510204 + -0.7142857143x + x2 = 21.5561224504 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 21.5561224504 Calculate the square root of the right side: 4.642857143 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 4.642857143 and -4.642857143.Subproblem 1
x + -0.3571428572 = 4.642857143 Simplifying x + -0.3571428572 = 4.642857143 Reorder the terms: -0.3571428572 + x = 4.642857143 Solving -0.3571428572 + x = 4.642857143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 4.642857143 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 4.642857143 + 0.3571428572 x = 4.642857143 + 0.3571428572 Combine like terms: 4.642857143 + 0.3571428572 = 5.0000000002 x = 5.0000000002 Simplifying x = 5.0000000002Subproblem 2
x + -0.3571428572 = -4.642857143 Simplifying x + -0.3571428572 = -4.642857143 Reorder the terms: -0.3571428572 + x = -4.642857143 Solving -0.3571428572 + x = -4.642857143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -4.642857143 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -4.642857143 + 0.3571428572 x = -4.642857143 + 0.3571428572 Combine like terms: -4.642857143 + 0.3571428572 = -4.2857142858 x = -4.2857142858 Simplifying x = -4.2857142858Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.0000000002, -4.2857142858}
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