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Simplifying 2x2 + 5x + 3 = 135 Reorder the terms: 3 + 5x + 2x2 = 135 Solving 3 + 5x + 2x2 = 135 Solving for variable 'x'. Reorder the terms: 3 + -135 + 5x + 2x2 = 135 + -135 Combine like terms: 3 + -135 = -132 -132 + 5x + 2x2 = 135 + -135 Combine like terms: 135 + -135 = 0 -132 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -66 + 2.5x + x2 = 0 Move the constant term to the right: Add '66' to each side of the equation. -66 + 2.5x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + 2.5x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 2.5x + x2 = 0 + 66 2.5x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 2.5x + x2 = 66 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 = 66 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 66 + 1.5625 Combine like terms: 66 + 1.5625 = 67.5625 1.5625 + 2.5x + x2 = 67.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 67.5625 Calculate the square root of the right side: 8.219641111 Break this problem into two subproblems by setting (x + 1.25) equal to 8.219641111 and -8.219641111.Subproblem 1
x + 1.25 = 8.219641111 Simplifying x + 1.25 = 8.219641111 Reorder the terms: 1.25 + x = 8.219641111 Solving 1.25 + x = 8.219641111 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 = 8.219641111 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 8.219641111 + -1.25 x = 8.219641111 + -1.25 Combine like terms: 8.219641111 + -1.25 = 6.969641111 x = 6.969641111 Simplifying x = 6.969641111Subproblem 2
x + 1.25 = -8.219641111 Simplifying x + 1.25 = -8.219641111 Reorder the terms: 1.25 + x = -8.219641111 Solving 1.25 + x = -8.219641111 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 = -8.219641111 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -8.219641111 + -1.25 x = -8.219641111 + -1.25 Combine like terms: -8.219641111 + -1.25 = -9.469641111 x = -9.469641111 Simplifying x = -9.469641111Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.969641111, -9.469641111}
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