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Simplifying 5x2 + 18x + -24 = 0 Reorder the terms: -24 + 18x + 5x2 = 0 Solving -24 + 18x + 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 + 3.6x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + 3.6x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + 3.6x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 3.6x + x2 = 0 + 4.8 3.6x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 3.6x + x2 = 4.8 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = 4.8 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 4.8 + 3.24 Combine like terms: 4.8 + 3.24 = 8.04 3.24 + 3.6x + x2 = 8.04 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 8.04 Calculate the square root of the right side: 2.835489376 Break this problem into two subproblems by setting (x + 1.8) equal to 2.835489376 and -2.835489376.Subproblem 1
x + 1.8 = 2.835489376 Simplifying x + 1.8 = 2.835489376 Reorder the terms: 1.8 + x = 2.835489376 Solving 1.8 + x = 2.835489376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 2.835489376 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 2.835489376 + -1.8 x = 2.835489376 + -1.8 Combine like terms: 2.835489376 + -1.8 = 1.035489376 x = 1.035489376 Simplifying x = 1.035489376Subproblem 2
x + 1.8 = -2.835489376 Simplifying x + 1.8 = -2.835489376 Reorder the terms: 1.8 + x = -2.835489376 Solving 1.8 + x = -2.835489376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -2.835489376 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -2.835489376 + -1.8 x = -2.835489376 + -1.8 Combine like terms: -2.835489376 + -1.8 = -4.635489376 x = -4.635489376 Simplifying x = -4.635489376Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.035489376, -4.635489376}
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