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Simplifying 2x + x2 = 0.079 Solving 2x + x2 = 0.079 Solving for variable 'x'. Reorder the terms: -0.079 + 2x + x2 = 0.079 + -0.079 Combine like terms: 0.079 + -0.079 = 0.000 -0.079 + 2x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '0.079' to each side of the equation. -0.079 + 2x + 0.079 + x2 = 0.000 + 0.079 Reorder the terms: -0.079 + 0.079 + 2x + x2 = 0.000 + 0.079 Combine like terms: -0.079 + 0.079 = 0.000 0.000 + 2x + x2 = 0.000 + 0.079 2x + x2 = 0.000 + 0.079 Combine like terms: 0.000 + 0.079 = 0.079 2x + x2 = 0.079 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 = 0.079 + 1 Reorder the terms: 1 + 2x + x2 = 0.079 + 1 Combine like terms: 0.079 + 1 = 1.079 1 + 2x + x2 = 1.079 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.079 Calculate the square root of the right side: 1.038749248 Break this problem into two subproblems by setting (x + 1) equal to 1.038749248 and -1.038749248.Subproblem 1
x + 1 = 1.038749248 Simplifying x + 1 = 1.038749248 Reorder the terms: 1 + x = 1.038749248 Solving 1 + x = 1.038749248 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 = 1.038749248 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.038749248 + -1 x = 1.038749248 + -1 Combine like terms: 1.038749248 + -1 = 0.038749248 x = 0.038749248 Simplifying x = 0.038749248Subproblem 2
x + 1 = -1.038749248 Simplifying x + 1 = -1.038749248 Reorder the terms: 1 + x = -1.038749248 Solving 1 + x = -1.038749248 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 = -1.038749248 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.038749248 + -1 x = -1.038749248 + -1 Combine like terms: -1.038749248 + -1 = -2.038749248 x = -2.038749248 Simplifying x = -2.038749248Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.038749248, -2.038749248}
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