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Simplifying 3x2 + -5x + -210 = 0 Reorder the terms: -210 + -5x + 3x2 = 0 Solving -210 + -5x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -70 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + -1.666666667x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + -1.666666667x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -1.666666667x + x2 = 0 + 70 -1.666666667x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 -1.666666667x + x2 = 70 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 70 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 70 + 0.6944444447 Combine like terms: 70 + 0.6944444447 = 70.6944444447 0.6944444447 + -1.666666667x + x2 = 70.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 70.6944444447 Calculate the square root of the right side: 8.407998837 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 8.407998837 and -8.407998837.Subproblem 1
x + -0.8333333335 = 8.407998837 Simplifying x + -0.8333333335 = 8.407998837 Reorder the terms: -0.8333333335 + x = 8.407998837 Solving -0.8333333335 + x = 8.407998837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 8.407998837 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 8.407998837 + 0.8333333335 x = 8.407998837 + 0.8333333335 Combine like terms: 8.407998837 + 0.8333333335 = 9.2413321705 x = 9.2413321705 Simplifying x = 9.2413321705Subproblem 2
x + -0.8333333335 = -8.407998837 Simplifying x + -0.8333333335 = -8.407998837 Reorder the terms: -0.8333333335 + x = -8.407998837 Solving -0.8333333335 + x = -8.407998837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -8.407998837 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -8.407998837 + 0.8333333335 x = -8.407998837 + 0.8333333335 Combine like terms: -8.407998837 + 0.8333333335 = -7.5746655035 x = -7.5746655035 Simplifying x = -7.5746655035Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.2413321705, -7.5746655035}
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