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Simplifying 4x2 + 3x + -520 = 0 Reorder the terms: -520 + 3x + 4x2 = 0 Solving -520 + 3x + 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 + 0.75x + x2 = 0 Move the constant term to the right: Add '130' to each side of the equation. -130 + 0.75x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 0.75x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 0.75x + x2 = 0 + 130 0.75x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 0.75x + x2 = 130 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 130 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 130 + 0.140625 Combine like terms: 130 + 0.140625 = 130.140625 0.140625 + 0.75x + x2 = 130.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 130.140625 Calculate the square root of the right side: 11.407919398 Break this problem into two subproblems by setting (x + 0.375) equal to 11.407919398 and -11.407919398.Subproblem 1
x + 0.375 = 11.407919398 Simplifying x + 0.375 = 11.407919398 Reorder the terms: 0.375 + x = 11.407919398 Solving 0.375 + x = 11.407919398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 11.407919398 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 11.407919398 + -0.375 x = 11.407919398 + -0.375 Combine like terms: 11.407919398 + -0.375 = 11.032919398 x = 11.032919398 Simplifying x = 11.032919398Subproblem 2
x + 0.375 = -11.407919398 Simplifying x + 0.375 = -11.407919398 Reorder the terms: 0.375 + x = -11.407919398 Solving 0.375 + x = -11.407919398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -11.407919398 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -11.407919398 + -0.375 x = -11.407919398 + -0.375 Combine like terms: -11.407919398 + -0.375 = -11.782919398 x = -11.782919398 Simplifying x = -11.782919398Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.032919398, -11.782919398}
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