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Simplifying 5x2 + 2x + -31 = 0 Reorder the terms: -31 + 2x + 5x2 = 0 Solving -31 + 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'. -6.2 + 0.4x + x2 = 0 Move the constant term to the right: Add '6.2' to each side of the equation. -6.2 + 0.4x + 6.2 + x2 = 0 + 6.2 Reorder the terms: -6.2 + 6.2 + 0.4x + x2 = 0 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + 0.4x + x2 = 0 + 6.2 0.4x + x2 = 0 + 6.2 Combine like terms: 0 + 6.2 = 6.2 0.4x + x2 = 6.2 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 = 6.2 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 6.2 + 0.04 Combine like terms: 6.2 + 0.04 = 6.24 0.04 + 0.4x + x2 = 6.24 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 6.24 Calculate the square root of the right side: 2.497999199 Break this problem into two subproblems by setting (x + 0.2) equal to 2.497999199 and -2.497999199.Subproblem 1
x + 0.2 = 2.497999199 Simplifying x + 0.2 = 2.497999199 Reorder the terms: 0.2 + x = 2.497999199 Solving 0.2 + x = 2.497999199 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 = 2.497999199 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 2.497999199 + -0.2 x = 2.497999199 + -0.2 Combine like terms: 2.497999199 + -0.2 = 2.297999199 x = 2.297999199 Simplifying x = 2.297999199Subproblem 2
x + 0.2 = -2.497999199 Simplifying x + 0.2 = -2.497999199 Reorder the terms: 0.2 + x = -2.497999199 Solving 0.2 + x = -2.497999199 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 = -2.497999199 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -2.497999199 + -0.2 x = -2.497999199 + -0.2 Combine like terms: -2.497999199 + -0.2 = -2.697999199 x = -2.697999199 Simplifying x = -2.697999199Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.297999199, -2.697999199}
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