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Simplifying 5x2 + -12x + -24 = 0 Reorder the terms: -24 + -12x + 5x2 = 0 Solving -24 + -12x + 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 + -2.4x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -2.4x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -2.4x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -2.4x + x2 = 0 + 4.8 -2.4x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -2.4x + x2 = 4.8 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 4.8 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 4.8 + 1.44 Combine like terms: 4.8 + 1.44 = 6.24 1.44 + -2.4x + x2 = 6.24 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 6.24 Calculate the square root of the right side: 2.497999199 Break this problem into two subproblems by setting (x + -1.2) equal to 2.497999199 and -2.497999199.Subproblem 1
x + -1.2 = 2.497999199 Simplifying x + -1.2 = 2.497999199 Reorder the terms: -1.2 + x = 2.497999199 Solving -1.2 + x = 2.497999199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 2.497999199 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 2.497999199 + 1.2 x = 2.497999199 + 1.2 Combine like terms: 2.497999199 + 1.2 = 3.697999199 x = 3.697999199 Simplifying x = 3.697999199Subproblem 2
x + -1.2 = -2.497999199 Simplifying x + -1.2 = -2.497999199 Reorder the terms: -1.2 + x = -2.497999199 Solving -1.2 + x = -2.497999199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -2.497999199 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -2.497999199 + 1.2 x = -2.497999199 + 1.2 Combine like terms: -2.497999199 + 1.2 = -1.297999199 x = -1.297999199 Simplifying x = -1.297999199Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.697999199, -1.297999199}
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