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Simplifying -6x2 + 20 = 43x Reorder the terms: 20 + -6x2 = 43x Solving 20 + -6x2 = 43x Solving for variable 'x'. Reorder the terms: 20 + -43x + -6x2 = 43x + -43x Combine like terms: 43x + -43x = 0 20 + -43x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -3.333333333 + 7.166666667x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 7.166666667x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 7.166666667x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 7.166666667x + x2 = 0 + 3.333333333 7.166666667x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 7.166666667x + x2 = 3.333333333 The x term is 7.166666667x. Take half its coefficient (3.583333334). Square it (12.84027778) and add it to both sides. Add '12.84027778' to each side of the equation. 7.166666667x + 12.84027778 + x2 = 3.333333333 + 12.84027778 Reorder the terms: 12.84027778 + 7.166666667x + x2 = 3.333333333 + 12.84027778 Combine like terms: 3.333333333 + 12.84027778 = 16.173611113 12.84027778 + 7.166666667x + x2 = 16.173611113 Factor a perfect square on the left side: (x + 3.583333334)(x + 3.583333334) = 16.173611113 Calculate the square root of the right side: 4.021642838 Break this problem into two subproblems by setting (x + 3.583333334) equal to 4.021642838 and -4.021642838.Subproblem 1
x + 3.583333334 = 4.021642838 Simplifying x + 3.583333334 = 4.021642838 Reorder the terms: 3.583333334 + x = 4.021642838 Solving 3.583333334 + x = 4.021642838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.583333334' to each side of the equation. 3.583333334 + -3.583333334 + x = 4.021642838 + -3.583333334 Combine like terms: 3.583333334 + -3.583333334 = 0.000000000 0.000000000 + x = 4.021642838 + -3.583333334 x = 4.021642838 + -3.583333334 Combine like terms: 4.021642838 + -3.583333334 = 0.438309504 x = 0.438309504 Simplifying x = 0.438309504Subproblem 2
x + 3.583333334 = -4.021642838 Simplifying x + 3.583333334 = -4.021642838 Reorder the terms: 3.583333334 + x = -4.021642838 Solving 3.583333334 + x = -4.021642838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.583333334' to each side of the equation. 3.583333334 + -3.583333334 + x = -4.021642838 + -3.583333334 Combine like terms: 3.583333334 + -3.583333334 = 0.000000000 0.000000000 + x = -4.021642838 + -3.583333334 x = -4.021642838 + -3.583333334 Combine like terms: -4.021642838 + -3.583333334 = -7.604976172 x = -7.604976172 Simplifying x = -7.604976172Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.438309504, -7.604976172}
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