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Simplifying 5x2 + 24x = 60 Reorder the terms: 24x + 5x2 = 60 Solving 24x + 5x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + 24x + 5x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 24x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12 + 4.8x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 4.8x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 4.8x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 4.8x + x2 = 0 + 12 4.8x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 4.8x + x2 = 12 The x term is 4.8x. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x + 5.76 + x2 = 12 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = 12 + 5.76 Combine like terms: 12 + 5.76 = 17.76 5.76 + 4.8x + x2 = 17.76 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 17.76 Calculate the square root of the right side: 4.214261501 Break this problem into two subproblems by setting (x + 2.4) equal to 4.214261501 and -4.214261501.Subproblem 1
x + 2.4 = 4.214261501 Simplifying x + 2.4 = 4.214261501 Reorder the terms: 2.4 + x = 4.214261501 Solving 2.4 + x = 4.214261501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = 4.214261501 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 4.214261501 + -2.4 x = 4.214261501 + -2.4 Combine like terms: 4.214261501 + -2.4 = 1.814261501 x = 1.814261501 Simplifying x = 1.814261501Subproblem 2
x + 2.4 = -4.214261501 Simplifying x + 2.4 = -4.214261501 Reorder the terms: 2.4 + x = -4.214261501 Solving 2.4 + x = -4.214261501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = -4.214261501 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -4.214261501 + -2.4 x = -4.214261501 + -2.4 Combine like terms: -4.214261501 + -2.4 = -6.614261501 x = -6.614261501 Simplifying x = -6.614261501Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.814261501, -6.614261501}
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