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Simplifying 3x2 + -5x + -21 = 0 Reorder the terms: -21 + -5x + 3x2 = 0 Solving -21 + -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'. -7 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -1.666666667x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -1.666666667x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1.666666667x + x2 = 0 + 7 -1.666666667x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1.666666667x + x2 = 7 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 = 7 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 7 + 0.6944444447 Combine like terms: 7 + 0.6944444447 = 7.6944444447 0.6944444447 + -1.666666667x + x2 = 7.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 7.6944444447 Calculate the square root of the right side: 2.773886163 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 2.773886163 and -2.773886163.Subproblem 1
x + -0.8333333335 = 2.773886163 Simplifying x + -0.8333333335 = 2.773886163 Reorder the terms: -0.8333333335 + x = 2.773886163 Solving -0.8333333335 + x = 2.773886163 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 = 2.773886163 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 2.773886163 + 0.8333333335 x = 2.773886163 + 0.8333333335 Combine like terms: 2.773886163 + 0.8333333335 = 3.6072194965 x = 3.6072194965 Simplifying x = 3.6072194965Subproblem 2
x + -0.8333333335 = -2.773886163 Simplifying x + -0.8333333335 = -2.773886163 Reorder the terms: -0.8333333335 + x = -2.773886163 Solving -0.8333333335 + x = -2.773886163 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 = -2.773886163 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -2.773886163 + 0.8333333335 x = -2.773886163 + 0.8333333335 Combine like terms: -2.773886163 + 0.8333333335 = -1.9405528295 x = -1.9405528295 Simplifying x = -1.9405528295Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6072194965, -1.9405528295}
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