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Simplifying x2 + -0.2x + -3 = 0 Reorder the terms: -3 + -0.2x + x2 = 0 Solving -3 + -0.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.2x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -0.2x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.2x + x2 = 0 + 3 -0.2x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.2x + x2 = 3 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 3 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 3 + 0.01 Combine like terms: 3 + 0.01 = 3.01 0.01 + -0.2x + x2 = 3.01 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 3.01 Calculate the square root of the right side: 1.734935157 Break this problem into two subproblems by setting (x + -0.1) equal to 1.734935157 and -1.734935157.Subproblem 1
x + -0.1 = 1.734935157 Simplifying x + -0.1 = 1.734935157 Reorder the terms: -0.1 + x = 1.734935157 Solving -0.1 + x = 1.734935157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.734935157 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.734935157 + 0.1 x = 1.734935157 + 0.1 Combine like terms: 1.734935157 + 0.1 = 1.834935157 x = 1.834935157 Simplifying x = 1.834935157Subproblem 2
x + -0.1 = -1.734935157 Simplifying x + -0.1 = -1.734935157 Reorder the terms: -0.1 + x = -1.734935157 Solving -0.1 + x = -1.734935157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.734935157 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.734935157 + 0.1 x = -1.734935157 + 0.1 Combine like terms: -1.734935157 + 0.1 = -1.634935157 x = -1.634935157 Simplifying x = -1.634935157Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.834935157, -1.634935157}
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