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Simplifying 7 + -3X = 8X2 Solving 7 + -3X = 8X2 Solving for variable 'X'. Combine like terms: 8X2 + -8X2 = 0 7 + -3X + -8X2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.875 + 0.375X + X2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 0.375X + 0.875 + X2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 0.375X + X2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 0.375X + X2 = 0 + 0.875 0.375X + X2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 0.375X + X2 = 0.875 The X term is 0.375X. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375X + 0.03515625 + X2 = 0.875 + 0.03515625 Reorder the terms: 0.03515625 + 0.375X + X2 = 0.875 + 0.03515625 Combine like terms: 0.875 + 0.03515625 = 0.91015625 0.03515625 + 0.375X + X2 = 0.91015625 Factor a perfect square on the left side: (X + 0.1875)(X + 0.1875) = 0.91015625 Calculate the square root of the right side: 0.954021095 Break this problem into two subproblems by setting (X + 0.1875) equal to 0.954021095 and -0.954021095.Subproblem 1
X + 0.1875 = 0.954021095 Simplifying X + 0.1875 = 0.954021095 Reorder the terms: 0.1875 + X = 0.954021095 Solving 0.1875 + X = 0.954021095 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + X = 0.954021095 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + X = 0.954021095 + -0.1875 X = 0.954021095 + -0.1875 Combine like terms: 0.954021095 + -0.1875 = 0.766521095 X = 0.766521095 Simplifying X = 0.766521095Subproblem 2
X + 0.1875 = -0.954021095 Simplifying X + 0.1875 = -0.954021095 Reorder the terms: 0.1875 + X = -0.954021095 Solving 0.1875 + X = -0.954021095 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + X = -0.954021095 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + X = -0.954021095 + -0.1875 X = -0.954021095 + -0.1875 Combine like terms: -0.954021095 + -0.1875 = -1.141521095 X = -1.141521095 Simplifying X = -1.141521095Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.766521095, -1.141521095}
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