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Simplifying 8.38x2 + 3.97x + -4.99 = 0 Reorder the terms: -4.99 + 3.97x + 8.38x2 = 0 Solving -4.99 + 3.97x + 8.38x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8.38 the coefficient of the squared term: Divide each side by '8.38'. -0.5954653938 + 0.4737470167x + x2 = 0 Move the constant term to the right: Add '0.5954653938' to each side of the equation. -0.5954653938 + 0.4737470167x + 0.5954653938 + x2 = 0 + 0.5954653938 Reorder the terms: -0.5954653938 + 0.5954653938 + 0.4737470167x + x2 = 0 + 0.5954653938 Combine like terms: -0.5954653938 + 0.5954653938 = 0.0000000000 0.0000000000 + 0.4737470167x + x2 = 0 + 0.5954653938 0.4737470167x + x2 = 0 + 0.5954653938 Combine like terms: 0 + 0.5954653938 = 0.5954653938 0.4737470167x + x2 = 0.5954653938 The x term is 0.4737470167x. Take half its coefficient (0.2368735084). Square it (0.05610905898) and add it to both sides. Add '0.05610905898' to each side of the equation. 0.4737470167x + 0.05610905898 + x2 = 0.5954653938 + 0.05610905898 Reorder the terms: 0.05610905898 + 0.4737470167x + x2 = 0.5954653938 + 0.05610905898 Combine like terms: 0.5954653938 + 0.05610905898 = 0.65157445278 0.05610905898 + 0.4737470167x + x2 = 0.65157445278 Factor a perfect square on the left side: (x + 0.2368735084)(x + 0.2368735084) = 0.65157445278 Calculate the square root of the right side: 0.807201618 Break this problem into two subproblems by setting (x + 0.2368735084) equal to 0.807201618 and -0.807201618.Subproblem 1
x + 0.2368735084 = 0.807201618 Simplifying x + 0.2368735084 = 0.807201618 Reorder the terms: 0.2368735084 + x = 0.807201618 Solving 0.2368735084 + x = 0.807201618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2368735084' to each side of the equation. 0.2368735084 + -0.2368735084 + x = 0.807201618 + -0.2368735084 Combine like terms: 0.2368735084 + -0.2368735084 = 0.0000000000 0.0000000000 + x = 0.807201618 + -0.2368735084 x = 0.807201618 + -0.2368735084 Combine like terms: 0.807201618 + -0.2368735084 = 0.5703281096 x = 0.5703281096 Simplifying x = 0.5703281096Subproblem 2
x + 0.2368735084 = -0.807201618 Simplifying x + 0.2368735084 = -0.807201618 Reorder the terms: 0.2368735084 + x = -0.807201618 Solving 0.2368735084 + x = -0.807201618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2368735084' to each side of the equation. 0.2368735084 + -0.2368735084 + x = -0.807201618 + -0.2368735084 Combine like terms: 0.2368735084 + -0.2368735084 = 0.0000000000 0.0000000000 + x = -0.807201618 + -0.2368735084 x = -0.807201618 + -0.2368735084 Combine like terms: -0.807201618 + -0.2368735084 = -1.0440751264 x = -1.0440751264 Simplifying x = -1.0440751264Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5703281096, -1.0440751264}
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