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Simplifying 5x2 + -2x + -365 = 0 Reorder the terms: -365 + -2x + 5x2 = 0 Solving -365 + -2x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -73 + -0.4x + x2 = 0 Move the constant term to the right: Add '73' to each side of the equation. -73 + -0.4x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + -0.4x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + -0.4x + x2 = 0 + 73 -0.4x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 -0.4x + x2 = 73 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 73 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 73 + 0.04 Combine like terms: 73 + 0.04 = 73.04 0.04 + -0.4x + x2 = 73.04 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 73.04 Calculate the square root of the right side: 8.546344248 Break this problem into two subproblems by setting (x + -0.2) equal to 8.546344248 and -8.546344248.Subproblem 1
x + -0.2 = 8.546344248 Simplifying x + -0.2 = 8.546344248 Reorder the terms: -0.2 + x = 8.546344248 Solving -0.2 + x = 8.546344248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 8.546344248 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 8.546344248 + 0.2 x = 8.546344248 + 0.2 Combine like terms: 8.546344248 + 0.2 = 8.746344248 x = 8.746344248 Simplifying x = 8.746344248Subproblem 2
x + -0.2 = -8.546344248 Simplifying x + -0.2 = -8.546344248 Reorder the terms: -0.2 + x = -8.546344248 Solving -0.2 + x = -8.546344248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -8.546344248 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -8.546344248 + 0.2 x = -8.546344248 + 0.2 Combine like terms: -8.546344248 + 0.2 = -8.346344248 x = -8.346344248 Simplifying x = -8.346344248Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.746344248, -8.346344248}
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