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Simplifying x2 + -1.3x + -0.3 = 0 Reorder the terms: -0.3 + -1.3x + x2 = 0 Solving -0.3 + -1.3x + 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 + -1.3x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + -1.3x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -1.3x + x2 = 0 + 0.3 -1.3x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 -1.3x + x2 = 0.3 The x term is -1.3x. Take half its coefficient (-0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. -1.3x + 0.4225 + x2 = 0.3 + 0.4225 Reorder the terms: 0.4225 + -1.3x + x2 = 0.3 + 0.4225 Combine like terms: 0.3 + 0.4225 = 0.7225 0.4225 + -1.3x + x2 = 0.7225 Factor a perfect square on the left side: (x + -0.65)(x + -0.65) = 0.7225 Calculate the square root of the right side: 0.85 Break this problem into two subproblems by setting (x + -0.65) equal to 0.85 and -0.85.Subproblem 1
x + -0.65 = 0.85 Simplifying x + -0.65 = 0.85 Reorder the terms: -0.65 + x = 0.85 Solving -0.65 + x = 0.85 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = 0.85 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = 0.85 + 0.65 x = 0.85 + 0.65 Combine like terms: 0.85 + 0.65 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + -0.65 = -0.85 Simplifying x + -0.65 = -0.85 Reorder the terms: -0.65 + x = -0.85 Solving -0.65 + x = -0.85 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = -0.85 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = -0.85 + 0.65 x = -0.85 + 0.65 Combine like terms: -0.85 + 0.65 = -0.2 x = -0.2 Simplifying x = -0.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, -0.2}
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