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Simplifying 4x2 + 7x + -520 = 0 Reorder the terms: -520 + 7x + 4x2 = 0 Solving -520 + 7x + 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 + 1.75x + x2 = 0 Move the constant term to the right: Add '130' to each side of the equation. -130 + 1.75x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 1.75x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 1.75x + x2 = 0 + 130 1.75x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 1.75x + x2 = 130 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 130 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 130 + 0.765625 Combine like terms: 130 + 0.765625 = 130.765625 0.765625 + 1.75x + x2 = 130.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 130.765625 Calculate the square root of the right side: 11.435279839 Break this problem into two subproblems by setting (x + 0.875) equal to 11.435279839 and -11.435279839.Subproblem 1
x + 0.875 = 11.435279839 Simplifying x + 0.875 = 11.435279839 Reorder the terms: 0.875 + x = 11.435279839 Solving 0.875 + x = 11.435279839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 11.435279839 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 11.435279839 + -0.875 x = 11.435279839 + -0.875 Combine like terms: 11.435279839 + -0.875 = 10.560279839 x = 10.560279839 Simplifying x = 10.560279839Subproblem 2
x + 0.875 = -11.435279839 Simplifying x + 0.875 = -11.435279839 Reorder the terms: 0.875 + x = -11.435279839 Solving 0.875 + x = -11.435279839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -11.435279839 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -11.435279839 + -0.875 x = -11.435279839 + -0.875 Combine like terms: -11.435279839 + -0.875 = -12.310279839 x = -12.310279839 Simplifying x = -12.310279839Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.560279839, -12.310279839}
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