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Simplifying 5x2 + 31x + -48 = 0 Reorder the terms: -48 + 31x + 5x2 = 0 Solving -48 + 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'. -9.6 + 6.2x + x2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + 6.2x + 9.6 + x2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + 6.2x + x2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + 6.2x + x2 = 0 + 9.6 6.2x + x2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 6.2x + x2 = 9.6 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 = 9.6 + 9.61 Reorder the terms: 9.61 + 6.2x + x2 = 9.6 + 9.61 Combine like terms: 9.6 + 9.61 = 19.21 9.61 + 6.2x + x2 = 19.21 Factor a perfect square on the left side: (x + 3.1)(x + 3.1) = 19.21 Calculate the square root of the right side: 4.3829214 Break this problem into two subproblems by setting (x + 3.1) equal to 4.3829214 and -4.3829214.Subproblem 1
x + 3.1 = 4.3829214 Simplifying x + 3.1 = 4.3829214 Reorder the terms: 3.1 + x = 4.3829214 Solving 3.1 + x = 4.3829214 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 = 4.3829214 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = 4.3829214 + -3.1 x = 4.3829214 + -3.1 Combine like terms: 4.3829214 + -3.1 = 1.2829214 x = 1.2829214 Simplifying x = 1.2829214Subproblem 2
x + 3.1 = -4.3829214 Simplifying x + 3.1 = -4.3829214 Reorder the terms: 3.1 + x = -4.3829214 Solving 3.1 + x = -4.3829214 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 = -4.3829214 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = -4.3829214 + -3.1 x = -4.3829214 + -3.1 Combine like terms: -4.3829214 + -3.1 = -7.4829214 x = -7.4829214 Simplifying x = -7.4829214Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2829214, -7.4829214}
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