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Simplifying 6x2 + 49x + 21 = 0 Reorder the terms: 21 + 49x + 6x2 = 0 Solving 21 + 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'. 3.5 + 8.166666667x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 8.166666667x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 8.166666667x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 8.166666667x + x2 = 0 + -3.5 8.166666667x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 8.166666667x + x2 = -3.5 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 = -3.5 + 16.67361112 Reorder the terms: 16.67361112 + 8.166666667x + x2 = -3.5 + 16.67361112 Combine like terms: -3.5 + 16.67361112 = 13.17361112 16.67361112 + 8.166666667x + x2 = 13.17361112 Factor a perfect square on the left side: (x + 4.083333334)(x + 4.083333334) = 13.17361112 Calculate the square root of the right side: 3.629546958 Break this problem into two subproblems by setting (x + 4.083333334) equal to 3.629546958 and -3.629546958.Subproblem 1
x + 4.083333334 = 3.629546958 Simplifying x + 4.083333334 = 3.629546958 Reorder the terms: 4.083333334 + x = 3.629546958 Solving 4.083333334 + x = 3.629546958 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 = 3.629546958 + -4.083333334 Combine like terms: 4.083333334 + -4.083333334 = 0.000000000 0.000000000 + x = 3.629546958 + -4.083333334 x = 3.629546958 + -4.083333334 Combine like terms: 3.629546958 + -4.083333334 = -0.453786376 x = -0.453786376 Simplifying x = -0.453786376Subproblem 2
x + 4.083333334 = -3.629546958 Simplifying x + 4.083333334 = -3.629546958 Reorder the terms: 4.083333334 + x = -3.629546958 Solving 4.083333334 + x = -3.629546958 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 = -3.629546958 + -4.083333334 Combine like terms: 4.083333334 + -4.083333334 = 0.000000000 0.000000000 + x = -3.629546958 + -4.083333334 x = -3.629546958 + -4.083333334 Combine like terms: -3.629546958 + -4.083333334 = -7.712880292 x = -7.712880292 Simplifying x = -7.712880292Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.453786376, -7.712880292}
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