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Simplifying 8x * x + -699x + -56624 = 0 Multiply x * x 8x2 + -699x + -56624 = 0 Reorder the terms: -56624 + -699x + 8x2 = 0 Solving -56624 + -699x + 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'. -7078 + -87.375x + x2 = 0 Move the constant term to the right: Add '7078' to each side of the equation. -7078 + -87.375x + 7078 + x2 = 0 + 7078 Reorder the terms: -7078 + 7078 + -87.375x + x2 = 0 + 7078 Combine like terms: -7078 + 7078 = 0 0 + -87.375x + x2 = 0 + 7078 -87.375x + x2 = 0 + 7078 Combine like terms: 0 + 7078 = 7078 -87.375x + x2 = 7078 The x term is -87.375x. Take half its coefficient (-43.6875). Square it (1908.597656) and add it to both sides. Add '1908.597656' to each side of the equation. -87.375x + 1908.597656 + x2 = 7078 + 1908.597656 Reorder the terms: 1908.597656 + -87.375x + x2 = 7078 + 1908.597656 Combine like terms: 7078 + 1908.597656 = 8986.597656 1908.597656 + -87.375x + x2 = 8986.597656 Factor a perfect square on the left side: (x + -43.6875)(x + -43.6875) = 8986.597656 Calculate the square root of the right side: 94.797666933 Break this problem into two subproblems by setting (x + -43.6875) equal to 94.797666933 and -94.797666933.Subproblem 1
x + -43.6875 = 94.797666933 Simplifying x + -43.6875 = 94.797666933 Reorder the terms: -43.6875 + x = 94.797666933 Solving -43.6875 + x = 94.797666933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '43.6875' to each side of the equation. -43.6875 + 43.6875 + x = 94.797666933 + 43.6875 Combine like terms: -43.6875 + 43.6875 = 0.0000 0.0000 + x = 94.797666933 + 43.6875 x = 94.797666933 + 43.6875 Combine like terms: 94.797666933 + 43.6875 = 138.485166933 x = 138.485166933 Simplifying x = 138.485166933Subproblem 2
x + -43.6875 = -94.797666933 Simplifying x + -43.6875 = -94.797666933 Reorder the terms: -43.6875 + x = -94.797666933 Solving -43.6875 + x = -94.797666933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '43.6875' to each side of the equation. -43.6875 + 43.6875 + x = -94.797666933 + 43.6875 Combine like terms: -43.6875 + 43.6875 = 0.0000 0.0000 + x = -94.797666933 + 43.6875 x = -94.797666933 + 43.6875 Combine like terms: -94.797666933 + 43.6875 = -51.110166933 x = -51.110166933 Simplifying x = -51.110166933Solution
The solution to the problem is based on the solutions from the subproblems. x = {138.485166933, -51.110166933}
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