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Simplifying 5x(3x + 5) = 13 Reorder the terms: 5x(5 + 3x) = 13 (5 * 5x + 3x * 5x) = 13 (25x + 15x2) = 13 Solving 25x + 15x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 25x + 15x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 25x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.8666666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '0.8666666667' to each side of the equation. -0.8666666667 + 1.666666667x + 0.8666666667 + x2 = 0 + 0.8666666667 Reorder the terms: -0.8666666667 + 0.8666666667 + 1.666666667x + x2 = 0 + 0.8666666667 Combine like terms: -0.8666666667 + 0.8666666667 = 0.0000000000 0.0000000000 + 1.666666667x + x2 = 0 + 0.8666666667 1.666666667x + x2 = 0 + 0.8666666667 Combine like terms: 0 + 0.8666666667 = 0.8666666667 1.666666667x + x2 = 0.8666666667 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 = 0.8666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 0.8666666667 + 0.6944444447 Combine like terms: 0.8666666667 + 0.6944444447 = 1.5611111114 0.6944444447 + 1.666666667x + x2 = 1.5611111114 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 1.5611111114 Calculate the square root of the right side: 1.249444321 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.249444321 and -1.249444321.Subproblem 1
x + 0.8333333335 = 1.249444321 Simplifying x + 0.8333333335 = 1.249444321 Reorder the terms: 0.8333333335 + x = 1.249444321 Solving 0.8333333335 + x = 1.249444321 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 = 1.249444321 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.249444321 + -0.8333333335 x = 1.249444321 + -0.8333333335 Combine like terms: 1.249444321 + -0.8333333335 = 0.4161109875 x = 0.4161109875 Simplifying x = 0.4161109875Subproblem 2
x + 0.8333333335 = -1.249444321 Simplifying x + 0.8333333335 = -1.249444321 Reorder the terms: 0.8333333335 + x = -1.249444321 Solving 0.8333333335 + x = -1.249444321 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 = -1.249444321 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.249444321 + -0.8333333335 x = -1.249444321 + -0.8333333335 Combine like terms: -1.249444321 + -0.8333333335 = -2.0827776545 x = -2.0827776545 Simplifying x = -2.0827776545Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4161109875, -2.0827776545}
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