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Simplifying X2 + 2X + -0.3 = 0 Reorder the terms: -0.3 + 2X + X2 = 0 Solving -0.3 + 2X + X2 = 0 Solving for variable 'X'. 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 + 0.3 Reorder the terms: -0.3 + 0.3 + 2X + X2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 2X + X2 = 0 + 0.3 2X + X2 = 0 + 0.3 Combine like terms: 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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