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Simplifying 4x + x2 = 92 Solving 4x + x2 = 92 Solving for variable 'x'. Reorder the terms: -92 + 4x + x2 = 92 + -92 Combine like terms: 92 + -92 = 0 -92 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + 4x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + 4x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 4x + x2 = 0 + 92 4x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 4x + x2 = 92 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 92 + 4 Reorder the terms: 4 + 4x + x2 = 92 + 4 Combine like terms: 92 + 4 = 96 4 + 4x + x2 = 96 Factor a perfect square on the left side: (x + 2)(x + 2) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + 2) equal to 9.797958971 and -9.797958971.Subproblem 1
x + 2 = 9.797958971 Simplifying x + 2 = 9.797958971 Reorder the terms: 2 + x = 9.797958971 Solving 2 + x = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 9.797958971 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.797958971 + -2 x = 9.797958971 + -2 Combine like terms: 9.797958971 + -2 = 7.797958971 x = 7.797958971 Simplifying x = 7.797958971Subproblem 2
x + 2 = -9.797958971 Simplifying x + 2 = -9.797958971 Reorder the terms: 2 + x = -9.797958971 Solving 2 + x = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -9.797958971 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.797958971 + -2 x = -9.797958971 + -2 Combine like terms: -9.797958971 + -2 = -11.797958971 x = -11.797958971 Simplifying x = -11.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.797958971, -11.797958971}
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