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Simplifying 5x2 + -1x + -236 = 0 Reorder the terms: -236 + -1x + 5x2 = 0 Solving -236 + -1x + 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'. -47.2 + -0.2x + x2 = 0 Move the constant term to the right: Add '47.2' to each side of the equation. -47.2 + -0.2x + 47.2 + x2 = 0 + 47.2 Reorder the terms: -47.2 + 47.2 + -0.2x + x2 = 0 + 47.2 Combine like terms: -47.2 + 47.2 = 0.0 0.0 + -0.2x + x2 = 0 + 47.2 -0.2x + x2 = 0 + 47.2 Combine like terms: 0 + 47.2 = 47.2 -0.2x + x2 = 47.2 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 = 47.2 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 47.2 + 0.01 Combine like terms: 47.2 + 0.01 = 47.21 0.01 + -0.2x + x2 = 47.21 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 47.21 Calculate the square root of the right side: 6.870953355 Break this problem into two subproblems by setting (x + -0.1) equal to 6.870953355 and -6.870953355.Subproblem 1
x + -0.1 = 6.870953355 Simplifying x + -0.1 = 6.870953355 Reorder the terms: -0.1 + x = 6.870953355 Solving -0.1 + x = 6.870953355 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 = 6.870953355 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 6.870953355 + 0.1 x = 6.870953355 + 0.1 Combine like terms: 6.870953355 + 0.1 = 6.970953355 x = 6.970953355 Simplifying x = 6.970953355Subproblem 2
x + -0.1 = -6.870953355 Simplifying x + -0.1 = -6.870953355 Reorder the terms: -0.1 + x = -6.870953355 Solving -0.1 + x = -6.870953355 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 = -6.870953355 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -6.870953355 + 0.1 x = -6.870953355 + 0.1 Combine like terms: -6.870953355 + 0.1 = -6.770953355 x = -6.770953355 Simplifying x = -6.770953355Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.970953355, -6.770953355}
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