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Simplifying 6x2 + 49x + 90 = 0 Reorder the terms: 90 + 49x + 6x2 = 0 Solving 90 + 49x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 15 + 8.166666667x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + 8.166666667x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 8.166666667x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 8.166666667x + x2 = 0 + -15 8.166666667x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 8.166666667x + x2 = -15 The x term is 8.166666667x. Take half its coefficient (4.083333334). Square it (16.67361112) and add it to both sides. Add '16.67361112' to each side of the equation. 8.166666667x + 16.67361112 + x2 = -15 + 16.67361112 Reorder the terms: 16.67361112 + 8.166666667x + x2 = -15 + 16.67361112 Combine like terms: -15 + 16.67361112 = 1.67361112 16.67361112 + 8.166666667x + x2 = 1.67361112 Factor a perfect square on the left side: (x + 4.083333334)(x + 4.083333334) = 1.67361112 Calculate the square root of the right side: 1.293681228 Break this problem into two subproblems by setting (x + 4.083333334) equal to 1.293681228 and -1.293681228.Subproblem 1
x + 4.083333334 = 1.293681228 Simplifying x + 4.083333334 = 1.293681228 Reorder the terms: 4.083333334 + x = 1.293681228 Solving 4.083333334 + x = 1.293681228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.083333334' to each side of the equation. 4.083333334 + -4.083333334 + x = 1.293681228 + -4.083333334 Combine like terms: 4.083333334 + -4.083333334 = 0.000000000 0.000000000 + x = 1.293681228 + -4.083333334 x = 1.293681228 + -4.083333334 Combine like terms: 1.293681228 + -4.083333334 = -2.789652106 x = -2.789652106 Simplifying x = -2.789652106Subproblem 2
x + 4.083333334 = -1.293681228 Simplifying x + 4.083333334 = -1.293681228 Reorder the terms: 4.083333334 + x = -1.293681228 Solving 4.083333334 + x = -1.293681228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.083333334' to each side of the equation. 4.083333334 + -4.083333334 + x = -1.293681228 + -4.083333334 Combine like terms: 4.083333334 + -4.083333334 = 0.000000000 0.000000000 + x = -1.293681228 + -4.083333334 x = -1.293681228 + -4.083333334 Combine like terms: -1.293681228 + -4.083333334 = -5.377014562 x = -5.377014562 Simplifying x = -5.377014562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.789652106, -5.377014562}
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