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Simplifying x2 + 2x = 0.3 Reorder the terms: 2x + x2 = 0.3 Solving 2x + x2 = 0.3 Solving for variable 'x'. Reorder the terms: -0.3 + 2x + x2 = 0.3 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 -0.3 + 2x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 2x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + 2x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 2x + x2 = 0.0 + 0.3 2x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 2x + x2 = 0.3 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 = 0.3 + 1 Reorder the terms: 1 + 2x + x2 = 0.3 + 1 Combine like terms: 0.3 + 1 = 1.3 1 + 2x + x2 = 1.3 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.3 Calculate the square root of the right side: 1.140175425 Break this problem into two subproblems by setting (x + 1) equal to 1.140175425 and -1.140175425.Subproblem 1
x + 1 = 1.140175425 Simplifying x + 1 = 1.140175425 Reorder the terms: 1 + x = 1.140175425 Solving 1 + x = 1.140175425 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 = 1.140175425 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.140175425 + -1 x = 1.140175425 + -1 Combine like terms: 1.140175425 + -1 = 0.140175425 x = 0.140175425 Simplifying x = 0.140175425Subproblem 2
x + 1 = -1.140175425 Simplifying x + 1 = -1.140175425 Reorder the terms: 1 + x = -1.140175425 Solving 1 + x = -1.140175425 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 = -1.140175425 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.140175425 + -1 x = -1.140175425 + -1 Combine like terms: -1.140175425 + -1 = -2.140175425 x = -2.140175425 Simplifying x = -2.140175425Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.140175425, -2.140175425}
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