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Simplifying x2 + -0.3x + -0.28 = 0 Reorder the terms: -0.28 + -0.3x + x2 = 0 Solving -0.28 + -0.3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.28' to each side of the equation. -0.28 + -0.3x + 0.28 + x2 = 0 + 0.28 Reorder the terms: -0.28 + 0.28 + -0.3x + x2 = 0 + 0.28 Combine like terms: -0.28 + 0.28 = 0.00 0.00 + -0.3x + x2 = 0 + 0.28 -0.3x + x2 = 0 + 0.28 Combine like terms: 0 + 0.28 = 0.28 -0.3x + x2 = 0.28 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 0.28 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 0.28 + 0.0225 Combine like terms: 0.28 + 0.0225 = 0.3025 0.0225 + -0.3x + x2 = 0.3025 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 0.3025 Calculate the square root of the right side: 0.55 Break this problem into two subproblems by setting (x + -0.15) equal to 0.55 and -0.55.Subproblem 1
x + -0.15 = 0.55 Simplifying x + -0.15 = 0.55 Reorder the terms: -0.15 + x = 0.55 Solving -0.15 + x = 0.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 0.55 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.55 + 0.15 x = 0.55 + 0.15 Combine like terms: 0.55 + 0.15 = 0.7 x = 0.7 Simplifying x = 0.7Subproblem 2
x + -0.15 = -0.55 Simplifying x + -0.15 = -0.55 Reorder the terms: -0.15 + x = -0.55 Solving -0.15 + x = -0.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -0.55 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.55 + 0.15 x = -0.55 + 0.15 Combine like terms: -0.55 + 0.15 = -0.4 x = -0.4 Simplifying x = -0.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7, -0.4}
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