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Simplifying 3x2 + -5x + -30 = 0 Reorder the terms: -30 + -5x + 3x2 = 0 Solving -30 + -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'. -10 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -1.666666667x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -1.666666667x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1.666666667x + x2 = 0 + 10 -1.666666667x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -1.666666667x + x2 = 10 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 = 10 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 10 + 0.6944444447 Combine like terms: 10 + 0.6944444447 = 10.6944444447 0.6944444447 + -1.666666667x + x2 = 10.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 10.6944444447 Calculate the square root of the right side: 3.270236145 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 3.270236145 and -3.270236145.Subproblem 1
x + -0.8333333335 = 3.270236145 Simplifying x + -0.8333333335 = 3.270236145 Reorder the terms: -0.8333333335 + x = 3.270236145 Solving -0.8333333335 + x = 3.270236145 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 = 3.270236145 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 3.270236145 + 0.8333333335 x = 3.270236145 + 0.8333333335 Combine like terms: 3.270236145 + 0.8333333335 = 4.1035694785 x = 4.1035694785 Simplifying x = 4.1035694785Subproblem 2
x + -0.8333333335 = -3.270236145 Simplifying x + -0.8333333335 = -3.270236145 Reorder the terms: -0.8333333335 + x = -3.270236145 Solving -0.8333333335 + x = -3.270236145 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 = -3.270236145 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -3.270236145 + 0.8333333335 x = -3.270236145 + 0.8333333335 Combine like terms: -3.270236145 + 0.8333333335 = -2.4369028115 x = -2.4369028115 Simplifying x = -2.4369028115Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.1035694785, -2.4369028115}
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