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Simplifying 5x2 + -24x + 24 = 0 Reorder the terms: 24 + -24x + 5x2 = 0 Solving 24 + -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'. 4.8 + -4.8x + x2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + -4.8x + -4.8 + x2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + -4.8x + x2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + -4.8x + x2 = 0 + -4.8 -4.8x + x2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 -4.8x + x2 = -4.8 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 = -4.8 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = -4.8 + 5.76 Combine like terms: -4.8 + 5.76 = 0.96 5.76 + -4.8x + x2 = 0.96 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (x + -2.4) equal to 0.979795897 and -0.979795897.Subproblem 1
x + -2.4 = 0.979795897 Simplifying x + -2.4 = 0.979795897 Reorder the terms: -2.4 + x = 0.979795897 Solving -2.4 + x = 0.979795897 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 = 0.979795897 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 0.979795897 + 2.4 x = 0.979795897 + 2.4 Combine like terms: 0.979795897 + 2.4 = 3.379795897 x = 3.379795897 Simplifying x = 3.379795897Subproblem 2
x + -2.4 = -0.979795897 Simplifying x + -2.4 = -0.979795897 Reorder the terms: -2.4 + x = -0.979795897 Solving -2.4 + x = -0.979795897 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 = -0.979795897 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -0.979795897 + 2.4 x = -0.979795897 + 2.4 Combine like terms: -0.979795897 + 2.4 = 1.420204103 x = 1.420204103 Simplifying x = 1.420204103Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.379795897, 1.420204103}
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