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Simplifying 5x2 + 6x + -31 = 0 Reorder the terms: -31 + 6x + 5x2 = 0 Solving -31 + 6x + 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 + 1.2x + x2 = 0 Move the constant term to the right: Add '6.2' to each side of the equation. -6.2 + 1.2x + 6.2 + x2 = 0 + 6.2 Reorder the terms: -6.2 + 6.2 + 1.2x + x2 = 0 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + 1.2x + x2 = 0 + 6.2 1.2x + x2 = 0 + 6.2 Combine like terms: 0 + 6.2 = 6.2 1.2x + x2 = 6.2 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 6.2 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 6.2 + 0.36 Combine like terms: 6.2 + 0.36 = 6.56 0.36 + 1.2x + x2 = 6.56 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 6.56 Calculate the square root of the right side: 2.561249695 Break this problem into two subproblems by setting (x + 0.6) equal to 2.561249695 and -2.561249695.Subproblem 1
x + 0.6 = 2.561249695 Simplifying x + 0.6 = 2.561249695 Reorder the terms: 0.6 + x = 2.561249695 Solving 0.6 + x = 2.561249695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 2.561249695 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 2.561249695 + -0.6 x = 2.561249695 + -0.6 Combine like terms: 2.561249695 + -0.6 = 1.961249695 x = 1.961249695 Simplifying x = 1.961249695Subproblem 2
x + 0.6 = -2.561249695 Simplifying x + 0.6 = -2.561249695 Reorder the terms: 0.6 + x = -2.561249695 Solving 0.6 + x = -2.561249695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -2.561249695 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -2.561249695 + -0.6 x = -2.561249695 + -0.6 Combine like terms: -2.561249695 + -0.6 = -3.161249695 x = -3.161249695 Simplifying x = -3.161249695Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.961249695, -3.161249695}
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