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Simplifying 5x + 3x2 = 96 Solving 5x + 3x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + 5x + 3x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -32 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 1.666666667x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 1.666666667x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 1.666666667x + x2 = 0 + 32 1.666666667x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 1.666666667x + x2 = 32 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 = 32 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 32 + 0.6944444447 Combine like terms: 32 + 0.6944444447 = 32.6944444447 0.6944444447 + 1.666666667x + x2 = 32.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 32.6944444447 Calculate the square root of the right side: 5.717905599 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 5.717905599 and -5.717905599.Subproblem 1
x + 0.8333333335 = 5.717905599 Simplifying x + 0.8333333335 = 5.717905599 Reorder the terms: 0.8333333335 + x = 5.717905599 Solving 0.8333333335 + x = 5.717905599 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 = 5.717905599 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 5.717905599 + -0.8333333335 x = 5.717905599 + -0.8333333335 Combine like terms: 5.717905599 + -0.8333333335 = 4.8845722655 x = 4.8845722655 Simplifying x = 4.8845722655Subproblem 2
x + 0.8333333335 = -5.717905599 Simplifying x + 0.8333333335 = -5.717905599 Reorder the terms: 0.8333333335 + x = -5.717905599 Solving 0.8333333335 + x = -5.717905599 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 = -5.717905599 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -5.717905599 + -0.8333333335 x = -5.717905599 + -0.8333333335 Combine like terms: -5.717905599 + -0.8333333335 = -6.5512389325 x = -6.5512389325 Simplifying x = -6.5512389325Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.8845722655, -6.5512389325}
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