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Simplifying 6x2 + -19x + -21 = 0 Reorder the terms: -21 + -19x + 6x2 = 0 Solving -21 + -19x + 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 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -3.166666667x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -3.166666667x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -3.166666667x + x2 = 0 + 3.5 -3.166666667x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -3.166666667x + x2 = 3.5 The x term is -3.166666667x. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667x + 2.506944447 + x2 = 3.5 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 3.5 + 2.506944447 Combine like terms: 3.5 + 2.506944447 = 6.006944447 2.506944447 + -3.166666667x + x2 = 6.006944447 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 6.006944447 Calculate the square root of the right side: 2.450906862 Break this problem into two subproblems by setting (x + -1.583333334) equal to 2.450906862 and -2.450906862.Subproblem 1
x + -1.583333334 = 2.450906862 Simplifying x + -1.583333334 = 2.450906862 Reorder the terms: -1.583333334 + x = 2.450906862 Solving -1.583333334 + x = 2.450906862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = 2.450906862 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 2.450906862 + 1.583333334 x = 2.450906862 + 1.583333334 Combine like terms: 2.450906862 + 1.583333334 = 4.034240196 x = 4.034240196 Simplifying x = 4.034240196Subproblem 2
x + -1.583333334 = -2.450906862 Simplifying x + -1.583333334 = -2.450906862 Reorder the terms: -1.583333334 + x = -2.450906862 Solving -1.583333334 + x = -2.450906862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = -2.450906862 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -2.450906862 + 1.583333334 x = -2.450906862 + 1.583333334 Combine like terms: -2.450906862 + 1.583333334 = -0.867573528 x = -0.867573528 Simplifying x = -0.867573528Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.034240196, -0.867573528}
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