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Simplifying 3x(4x + 5) = 98 Reorder the terms: 3x(5 + 4x) = 98 (5 * 3x + 4x * 3x) = 98 (15x + 12x2) = 98 Solving 15x + 12x2 = 98 Solving for variable 'x'. Reorder the terms: -98 + 15x + 12x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + 15x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -8.166666667 + 1.25x + x2 = 0 Move the constant term to the right: Add '8.166666667' to each side of the equation. -8.166666667 + 1.25x + 8.166666667 + x2 = 0 + 8.166666667 Reorder the terms: -8.166666667 + 8.166666667 + 1.25x + x2 = 0 + 8.166666667 Combine like terms: -8.166666667 + 8.166666667 = 0.000000000 0.000000000 + 1.25x + x2 = 0 + 8.166666667 1.25x + x2 = 0 + 8.166666667 Combine like terms: 0 + 8.166666667 = 8.166666667 1.25x + x2 = 8.166666667 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 8.166666667 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 8.166666667 + 0.390625 Combine like terms: 8.166666667 + 0.390625 = 8.557291667 0.390625 + 1.25x + x2 = 8.557291667 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 8.557291667 Calculate the square root of the right side: 2.925284886 Break this problem into two subproblems by setting (x + 0.625) equal to 2.925284886 and -2.925284886.Subproblem 1
x + 0.625 = 2.925284886 Simplifying x + 0.625 = 2.925284886 Reorder the terms: 0.625 + x = 2.925284886 Solving 0.625 + x = 2.925284886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 2.925284886 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 2.925284886 + -0.625 x = 2.925284886 + -0.625 Combine like terms: 2.925284886 + -0.625 = 2.300284886 x = 2.300284886 Simplifying x = 2.300284886Subproblem 2
x + 0.625 = -2.925284886 Simplifying x + 0.625 = -2.925284886 Reorder the terms: 0.625 + x = -2.925284886 Solving 0.625 + x = -2.925284886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -2.925284886 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -2.925284886 + -0.625 x = -2.925284886 + -0.625 Combine like terms: -2.925284886 + -0.625 = -3.550284886 x = -3.550284886 Simplifying x = -3.550284886Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.300284886, -3.550284886}
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