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Simplifying 2x2 + 5x + -2 = 66 Reorder the terms: -2 + 5x + 2x2 = 66 Solving -2 + 5x + 2x2 = 66 Solving for variable 'x'. Reorder the terms: -2 + -66 + 5x + 2x2 = 66 + -66 Combine like terms: -2 + -66 = -68 -68 + 5x + 2x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -68 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -34 + 2.5x + x2 = 0 Move the constant term to the right: Add '34' to each side of the equation. -34 + 2.5x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + 2.5x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 2.5x + x2 = 0 + 34 2.5x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 2.5x + x2 = 34 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 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 34 + 1.5625 Combine like terms: 34 + 1.5625 = 35.5625 1.5625 + 2.5x + x2 = 35.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 35.5625 Calculate the square root of the right side: 5.963430221 Break this problem into two subproblems by setting (x + 1.25) equal to 5.963430221 and -5.963430221.Subproblem 1
x + 1.25 = 5.963430221 Simplifying x + 1.25 = 5.963430221 Reorder the terms: 1.25 + x = 5.963430221 Solving 1.25 + x = 5.963430221 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 = 5.963430221 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 5.963430221 + -1.25 x = 5.963430221 + -1.25 Combine like terms: 5.963430221 + -1.25 = 4.713430221 x = 4.713430221 Simplifying x = 4.713430221Subproblem 2
x + 1.25 = -5.963430221 Simplifying x + 1.25 = -5.963430221 Reorder the terms: 1.25 + x = -5.963430221 Solving 1.25 + x = -5.963430221 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 = -5.963430221 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -5.963430221 + -1.25 x = -5.963430221 + -1.25 Combine like terms: -5.963430221 + -1.25 = -7.213430221 x = -7.213430221 Simplifying x = -7.213430221Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.713430221, -7.213430221}
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