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Simplifying 5x2 + 31x + -7 = 0 Reorder the terms: -7 + 31x + 5x2 = 0 Solving -7 + 31x + 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'. -1.4 + 6.2x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 6.2x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 6.2x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 6.2x + x2 = 0 + 1.4 6.2x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 6.2x + x2 = 1.4 The x term is 6.2x. Take half its coefficient (3.1). Square it (9.61) and add it to both sides. Add '9.61' to each side of the equation. 6.2x + 9.61 + x2 = 1.4 + 9.61 Reorder the terms: 9.61 + 6.2x + x2 = 1.4 + 9.61 Combine like terms: 1.4 + 9.61 = 11.01 9.61 + 6.2x + x2 = 11.01 Factor a perfect square on the left side: (x + 3.1)(x + 3.1) = 11.01 Calculate the square root of the right side: 3.318132005 Break this problem into two subproblems by setting (x + 3.1) equal to 3.318132005 and -3.318132005.Subproblem 1
x + 3.1 = 3.318132005 Simplifying x + 3.1 = 3.318132005 Reorder the terms: 3.1 + x = 3.318132005 Solving 3.1 + x = 3.318132005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + x = 3.318132005 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = 3.318132005 + -3.1 x = 3.318132005 + -3.1 Combine like terms: 3.318132005 + -3.1 = 0.218132005 x = 0.218132005 Simplifying x = 0.218132005Subproblem 2
x + 3.1 = -3.318132005 Simplifying x + 3.1 = -3.318132005 Reorder the terms: 3.1 + x = -3.318132005 Solving 3.1 + x = -3.318132005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + x = -3.318132005 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = -3.318132005 + -3.1 x = -3.318132005 + -3.1 Combine like terms: -3.318132005 + -3.1 = -6.418132005 x = -6.418132005 Simplifying x = -6.418132005Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.218132005, -6.418132005}
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