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Simplifying 4x2 + 9x + -520 = 0 Reorder the terms: -520 + 9x + 4x2 = 0 Solving -520 + 9x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -130 + 2.25x + x2 = 0 Move the constant term to the right: Add '130' to each side of the equation. -130 + 2.25x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 2.25x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 2.25x + x2 = 0 + 130 2.25x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 2.25x + x2 = 130 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 = 130 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 130 + 1.265625 Combine like terms: 130 + 1.265625 = 131.265625 1.265625 + 2.25x + x2 = 131.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 131.265625 Calculate the square root of the right side: 11.457121148 Break this problem into two subproblems by setting (x + 1.125) equal to 11.457121148 and -11.457121148.Subproblem 1
x + 1.125 = 11.457121148 Simplifying x + 1.125 = 11.457121148 Reorder the terms: 1.125 + x = 11.457121148 Solving 1.125 + x = 11.457121148 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 = 11.457121148 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 11.457121148 + -1.125 x = 11.457121148 + -1.125 Combine like terms: 11.457121148 + -1.125 = 10.332121148 x = 10.332121148 Simplifying x = 10.332121148Subproblem 2
x + 1.125 = -11.457121148 Simplifying x + 1.125 = -11.457121148 Reorder the terms: 1.125 + x = -11.457121148 Solving 1.125 + x = -11.457121148 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 = -11.457121148 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -11.457121148 + -1.125 x = -11.457121148 + -1.125 Combine like terms: -11.457121148 + -1.125 = -12.582121148 x = -12.582121148 Simplifying x = -12.582121148Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.332121148, -12.582121148}
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