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Simplifying 5x2 + 21x + -24 = 0 Reorder the terms: -24 + 21x + 5x2 = 0 Solving -24 + 21x + 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'. -4.8 + 4.2x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + 4.2x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + 4.2x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 4.2x + x2 = 0 + 4.8 4.2x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 4.2x + x2 = 4.8 The x term is 4.2x. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2x + 4.41 + x2 = 4.8 + 4.41 Reorder the terms: 4.41 + 4.2x + x2 = 4.8 + 4.41 Combine like terms: 4.8 + 4.41 = 9.21 4.41 + 4.2x + x2 = 9.21 Factor a perfect square on the left side: (x + 2.1)(x + 2.1) = 9.21 Calculate the square root of the right side: 3.034798181 Break this problem into two subproblems by setting (x + 2.1) equal to 3.034798181 and -3.034798181.Subproblem 1
x + 2.1 = 3.034798181 Simplifying x + 2.1 = 3.034798181 Reorder the terms: 2.1 + x = 3.034798181 Solving 2.1 + x = 3.034798181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = 3.034798181 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 3.034798181 + -2.1 x = 3.034798181 + -2.1 Combine like terms: 3.034798181 + -2.1 = 0.934798181 x = 0.934798181 Simplifying x = 0.934798181Subproblem 2
x + 2.1 = -3.034798181 Simplifying x + 2.1 = -3.034798181 Reorder the terms: 2.1 + x = -3.034798181 Solving 2.1 + x = -3.034798181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = -3.034798181 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -3.034798181 + -2.1 x = -3.034798181 + -2.1 Combine like terms: -3.034798181 + -2.1 = -5.134798181 x = -5.134798181 Simplifying x = -5.134798181Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.934798181, -5.134798181}
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