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Simplifying 2x2 + 5x + -60 = 0 Reorder the terms: -60 + 5x + 2x2 = 0 Solving -60 + 5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -30 + 2.5x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 2.5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 2.5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 2.5x + x2 = 0 + 30 2.5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 2.5x + x2 = 30 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 30 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 30 + 1.5625 Combine like terms: 30 + 1.5625 = 31.5625 1.5625 + 2.5x + x2 = 31.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 31.5625 Calculate the square root of the right side: 5.618051264 Break this problem into two subproblems by setting (x + 1.25) equal to 5.618051264 and -5.618051264.Subproblem 1
x + 1.25 = 5.618051264 Simplifying x + 1.25 = 5.618051264 Reorder the terms: 1.25 + x = 5.618051264 Solving 1.25 + x = 5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 5.618051264 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 5.618051264 + -1.25 x = 5.618051264 + -1.25 Combine like terms: 5.618051264 + -1.25 = 4.368051264 x = 4.368051264 Simplifying x = 4.368051264Subproblem 2
x + 1.25 = -5.618051264 Simplifying x + 1.25 = -5.618051264 Reorder the terms: 1.25 + x = -5.618051264 Solving 1.25 + x = -5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -5.618051264 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -5.618051264 + -1.25 x = -5.618051264 + -1.25 Combine like terms: -5.618051264 + -1.25 = -6.868051264 x = -6.868051264 Simplifying x = -6.868051264Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.368051264, -6.868051264}
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