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Simplifying (4x + (x2) + -0.2342) = 0 (4x + x2 + -0.2342) = 0 Reorder the terms: (-0.2342 + 4x + x2) = 0 Remove parenthesis around (-0.2342 + 4x + x2) -0.2342 + 4x + x2 = 0 Solving -0.2342 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.2342' to each side of the equation. -0.2342 + 4x + 0.2342 + x2 = 0 + 0.2342 Reorder the terms: -0.2342 + 0.2342 + 4x + x2 = 0 + 0.2342 Combine like terms: -0.2342 + 0.2342 = 0.0000 0.0000 + 4x + x2 = 0 + 0.2342 4x + x2 = 0 + 0.2342 Combine like terms: 0 + 0.2342 = 0.2342 4x + x2 = 0.2342 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 = 0.2342 + 4 Reorder the terms: 4 + 4x + x2 = 0.2342 + 4 Combine like terms: 0.2342 + 4 = 4.2342 4 + 4x + x2 = 4.2342 Factor a perfect square on the left side: (x + 2)(x + 2) = 4.2342 Calculate the square root of the right side: 2.057717182 Break this problem into two subproblems by setting (x + 2) equal to 2.057717182 and -2.057717182.Subproblem 1
x + 2 = 2.057717182 Simplifying x + 2 = 2.057717182 Reorder the terms: 2 + x = 2.057717182 Solving 2 + x = 2.057717182 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 = 2.057717182 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.057717182 + -2 x = 2.057717182 + -2 Combine like terms: 2.057717182 + -2 = 0.057717182 x = 0.057717182 Simplifying x = 0.057717182Subproblem 2
x + 2 = -2.057717182 Simplifying x + 2 = -2.057717182 Reorder the terms: 2 + x = -2.057717182 Solving 2 + x = -2.057717182 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 = -2.057717182 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.057717182 + -2 x = -2.057717182 + -2 Combine like terms: -2.057717182 + -2 = -4.057717182 x = -4.057717182 Simplifying x = -4.057717182Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.057717182, -4.057717182}
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