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Simplifying x2 + 2x + -20 = 48 Reorder the terms: -20 + 2x + x2 = 48 Solving -20 + 2x + x2 = 48 Solving for variable 'x'. Reorder the terms: -20 + -48 + 2x + x2 = 48 + -48 Combine like terms: -20 + -48 = -68 -68 + 2x + x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -68 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + 2x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + 2x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + 2x + x2 = 0 + 68 2x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 2x + x2 = 68 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 68 + 1 Reorder the terms: 1 + 2x + x2 = 68 + 1 Combine like terms: 68 + 1 = 69 1 + 2x + x2 = 69 Factor a perfect square on the left side: (x + 1)(x + 1) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + 1) equal to 8.306623863 and -8.306623863.Subproblem 1
x + 1 = 8.306623863 Simplifying x + 1 = 8.306623863 Reorder the terms: 1 + x = 8.306623863 Solving 1 + x = 8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 8.306623863 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.306623863 + -1 x = 8.306623863 + -1 Combine like terms: 8.306623863 + -1 = 7.306623863 x = 7.306623863 Simplifying x = 7.306623863Subproblem 2
x + 1 = -8.306623863 Simplifying x + 1 = -8.306623863 Reorder the terms: 1 + x = -8.306623863 Solving 1 + x = -8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -8.306623863 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.306623863 + -1 x = -8.306623863 + -1 Combine like terms: -8.306623863 + -1 = -9.306623863 x = -9.306623863 Simplifying x = -9.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.306623863, -9.306623863}
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