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Simplifying -5x2 + -24x + 51 = 0 Reorder the terms: 51 + -24x + -5x2 = 0 Solving 51 + -24x + -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'. -10.2 + 4.8x + x2 = 0 Move the constant term to the right: Add '10.2' to each side of the equation. -10.2 + 4.8x + 10.2 + x2 = 0 + 10.2 Reorder the terms: -10.2 + 10.2 + 4.8x + x2 = 0 + 10.2 Combine like terms: -10.2 + 10.2 = 0.0 0.0 + 4.8x + x2 = 0 + 10.2 4.8x + x2 = 0 + 10.2 Combine like terms: 0 + 10.2 = 10.2 4.8x + x2 = 10.2 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 = 10.2 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = 10.2 + 5.76 Combine like terms: 10.2 + 5.76 = 15.96 5.76 + 4.8x + x2 = 15.96 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 15.96 Calculate the square root of the right side: 3.994996871 Break this problem into two subproblems by setting (x + 2.4) equal to 3.994996871 and -3.994996871.Subproblem 1
x + 2.4 = 3.994996871 Simplifying x + 2.4 = 3.994996871 Reorder the terms: 2.4 + x = 3.994996871 Solving 2.4 + x = 3.994996871 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 = 3.994996871 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 3.994996871 + -2.4 x = 3.994996871 + -2.4 Combine like terms: 3.994996871 + -2.4 = 1.594996871 x = 1.594996871 Simplifying x = 1.594996871Subproblem 2
x + 2.4 = -3.994996871 Simplifying x + 2.4 = -3.994996871 Reorder the terms: 2.4 + x = -3.994996871 Solving 2.4 + x = -3.994996871 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 = -3.994996871 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -3.994996871 + -2.4 x = -3.994996871 + -2.4 Combine like terms: -3.994996871 + -2.4 = -6.394996871 x = -6.394996871 Simplifying x = -6.394996871Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.594996871, -6.394996871}
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