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Simplifying 8x2 + -18x + -7 = 0 Reorder the terms: -7 + -18x + 8x2 = 0 Solving -7 + -18x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -2.25x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -2.25x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -2.25x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -2.25x + x2 = 0 + 0.875 -2.25x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -2.25x + x2 = 0.875 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 0.875 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 0.875 + 1.265625 Combine like terms: 0.875 + 1.265625 = 2.140625 1.265625 + -2.25x + x2 = 2.140625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (x + -1.125) equal to 1.463087489 and -1.463087489.Subproblem 1
x + -1.125 = 1.463087489 Simplifying x + -1.125 = 1.463087489 Reorder the terms: -1.125 + x = 1.463087489 Solving -1.125 + x = 1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.463087489 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.463087489 + 1.125 x = 1.463087489 + 1.125 Combine like terms: 1.463087489 + 1.125 = 2.588087489 x = 2.588087489 Simplifying x = 2.588087489Subproblem 2
x + -1.125 = -1.463087489 Simplifying x + -1.125 = -1.463087489 Reorder the terms: -1.125 + x = -1.463087489 Solving -1.125 + x = -1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.463087489 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.463087489 + 1.125 x = -1.463087489 + 1.125 Combine like terms: -1.463087489 + 1.125 = -0.338087489 x = -0.338087489 Simplifying x = -0.338087489Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.588087489, -0.338087489}
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