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Simplifying 2x2 + 5x + -4 = 65 Reorder the terms: -4 + 5x + 2x2 = 65 Solving -4 + 5x + 2x2 = 65 Solving for variable 'x'. Reorder the terms: -4 + -65 + 5x + 2x2 = 65 + -65 Combine like terms: -4 + -65 = -69 -69 + 5x + 2x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -69 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -34.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '34.5' to each side of the equation. -34.5 + 2.5x + 34.5 + x2 = 0 + 34.5 Reorder the terms: -34.5 + 34.5 + 2.5x + x2 = 0 + 34.5 Combine like terms: -34.5 + 34.5 = 0.0 0.0 + 2.5x + x2 = 0 + 34.5 2.5x + x2 = 0 + 34.5 Combine like terms: 0 + 34.5 = 34.5 2.5x + x2 = 34.5 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 = 34.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 34.5 + 1.5625 Combine like terms: 34.5 + 1.5625 = 36.0625 1.5625 + 2.5x + x2 = 36.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 36.0625 Calculate the square root of the right side: 6.005206075 Break this problem into two subproblems by setting (x + 1.25) equal to 6.005206075 and -6.005206075.Subproblem 1
x + 1.25 = 6.005206075 Simplifying x + 1.25 = 6.005206075 Reorder the terms: 1.25 + x = 6.005206075 Solving 1.25 + x = 6.005206075 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 = 6.005206075 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 6.005206075 + -1.25 x = 6.005206075 + -1.25 Combine like terms: 6.005206075 + -1.25 = 4.755206075 x = 4.755206075 Simplifying x = 4.755206075Subproblem 2
x + 1.25 = -6.005206075 Simplifying x + 1.25 = -6.005206075 Reorder the terms: 1.25 + x = -6.005206075 Solving 1.25 + x = -6.005206075 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 = -6.005206075 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -6.005206075 + -1.25 x = -6.005206075 + -1.25 Combine like terms: -6.005206075 + -1.25 = -7.255206075 x = -7.255206075 Simplifying x = -7.255206075Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.755206075, -7.255206075}
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