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Simplifying 3x2 + 5x + -72 = 0 Reorder the terms: -72 + 5x + 3x2 = 0 Solving -72 + 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'. -24 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 1.666666667x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 1.666666667x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 1.666666667x + x2 = 0 + 24 1.666666667x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 1.666666667x + x2 = 24 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 = 24 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 24 + 0.6944444447 Combine like terms: 24 + 0.6944444447 = 24.6944444447 0.6944444447 + 1.666666667x + x2 = 24.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 24.6944444447 Calculate the square root of the right side: 4.969350505 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 4.969350505 and -4.969350505.Subproblem 1
x + 0.8333333335 = 4.969350505 Simplifying x + 0.8333333335 = 4.969350505 Reorder the terms: 0.8333333335 + x = 4.969350505 Solving 0.8333333335 + x = 4.969350505 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 = 4.969350505 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 4.969350505 + -0.8333333335 x = 4.969350505 + -0.8333333335 Combine like terms: 4.969350505 + -0.8333333335 = 4.1360171715 x = 4.1360171715 Simplifying x = 4.1360171715Subproblem 2
x + 0.8333333335 = -4.969350505 Simplifying x + 0.8333333335 = -4.969350505 Reorder the terms: 0.8333333335 + x = -4.969350505 Solving 0.8333333335 + x = -4.969350505 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 = -4.969350505 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -4.969350505 + -0.8333333335 x = -4.969350505 + -0.8333333335 Combine like terms: -4.969350505 + -0.8333333335 = -5.8026838385 x = -5.8026838385 Simplifying x = -5.8026838385Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.1360171715, -5.8026838385}
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