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Simplifying 4x2 + 25x + -60 = 0 Reorder the terms: -60 + 25x + 4x2 = 0 Solving -60 + 25x + 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'. -15 + 6.25x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 6.25x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 6.25x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 6.25x + x2 = 0 + 15 6.25x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 6.25x + x2 = 15 The x term is 6.25x. Take half its coefficient (3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. 6.25x + 9.765625 + x2 = 15 + 9.765625 Reorder the terms: 9.765625 + 6.25x + x2 = 15 + 9.765625 Combine like terms: 15 + 9.765625 = 24.765625 9.765625 + 6.25x + x2 = 24.765625 Factor a perfect square on the left side: (x + 3.125)(x + 3.125) = 24.765625 Calculate the square root of the right side: 4.976507309 Break this problem into two subproblems by setting (x + 3.125) equal to 4.976507309 and -4.976507309.Subproblem 1
x + 3.125 = 4.976507309 Simplifying x + 3.125 = 4.976507309 Reorder the terms: 3.125 + x = 4.976507309 Solving 3.125 + x = 4.976507309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = 4.976507309 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = 4.976507309 + -3.125 x = 4.976507309 + -3.125 Combine like terms: 4.976507309 + -3.125 = 1.851507309 x = 1.851507309 Simplifying x = 1.851507309Subproblem 2
x + 3.125 = -4.976507309 Simplifying x + 3.125 = -4.976507309 Reorder the terms: 3.125 + x = -4.976507309 Solving 3.125 + x = -4.976507309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = -4.976507309 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = -4.976507309 + -3.125 x = -4.976507309 + -3.125 Combine like terms: -4.976507309 + -3.125 = -8.101507309 x = -8.101507309 Simplifying x = -8.101507309Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.851507309, -8.101507309}
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