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Simplifying 2X(5X + 8) = 71 Reorder the terms: 2X(8 + 5X) = 71 (8 * 2X + 5X * 2X) = 71 (16X + 10X2) = 71 Solving 16X + 10X2 = 71 Solving for variable 'X'. Reorder the terms: -71 + 16X + 10X2 = 71 + -71 Combine like terms: 71 + -71 = 0 -71 + 16X + 10X2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -7.1 + 1.6X + X2 = 0.0 Move the constant term to the right: Add '7.1' to each side of the equation. -7.1 + 1.6X + 7.1 + X2 = 0.0 + 7.1 Reorder the terms: -7.1 + 7.1 + 1.6X + X2 = 0.0 + 7.1 Combine like terms: -7.1 + 7.1 = 0.0 0.0 + 1.6X + X2 = 0.0 + 7.1 1.6X + X2 = 0.0 + 7.1 Combine like terms: 0.0 + 7.1 = 7.1 1.6X + X2 = 7.1 The X term is 1.6X. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6X + 0.64 + X2 = 7.1 + 0.64 Reorder the terms: 0.64 + 1.6X + X2 = 7.1 + 0.64 Combine like terms: 7.1 + 0.64 = 7.74 0.64 + 1.6X + X2 = 7.74 Factor a perfect square on the left side: (X + 0.8)(X + 0.8) = 7.74 Calculate the square root of the right side: 2.782085549 Break this problem into two subproblems by setting (X + 0.8) equal to 2.782085549 and -2.782085549.Subproblem 1
X + 0.8 = 2.782085549 Simplifying X + 0.8 = 2.782085549 Reorder the terms: 0.8 + X = 2.782085549 Solving 0.8 + X = 2.782085549 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + X = 2.782085549 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + X = 2.782085549 + -0.8 X = 2.782085549 + -0.8 Combine like terms: 2.782085549 + -0.8 = 1.982085549 X = 1.982085549 Simplifying X = 1.982085549Subproblem 2
X + 0.8 = -2.782085549 Simplifying X + 0.8 = -2.782085549 Reorder the terms: 0.8 + X = -2.782085549 Solving 0.8 + X = -2.782085549 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + X = -2.782085549 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + X = -2.782085549 + -0.8 X = -2.782085549 + -0.8 Combine like terms: -2.782085549 + -0.8 = -3.582085549 X = -3.582085549 Simplifying X = -3.582085549Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.982085549, -3.582085549}
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