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Simplifying 5x2 + 5x + -144 = 0 Reorder the terms: -144 + 5x + 5x2 = 0 Solving -144 + 5x + 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'. -28.8 + x + x2 = 0 Move the constant term to the right: Add '28.8' to each side of the equation. -28.8 + x + 28.8 + x2 = 0 + 28.8 Reorder the terms: -28.8 + 28.8 + x + x2 = 0 + 28.8 Combine like terms: -28.8 + 28.8 = 0.0 0.0 + x + x2 = 0 + 28.8 x + x2 = 0 + 28.8 Combine like terms: 0 + 28.8 = 28.8 x + x2 = 28.8 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 28.8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 28.8 + 0.25 Combine like terms: 28.8 + 0.25 = 29.05 1.25 + x2 = 29.05 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 29.05 Calculate the square root of the right side: 5.389805191 Break this problem into two subproblems by setting (x + 0.5) equal to 5.389805191 and -5.389805191.Subproblem 1
x + 0.5 = 5.389805191 Simplifying x + 0.5 = 5.389805191 Reorder the terms: 0.5 + x = 5.389805191 Solving 0.5 + x = 5.389805191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.389805191 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.389805191 + -0.5 x = 5.389805191 + -0.5 Combine like terms: 5.389805191 + -0.5 = 4.889805191 x = 4.889805191 Simplifying x = 4.889805191Subproblem 2
x + 0.5 = -5.389805191 Simplifying x + 0.5 = -5.389805191 Reorder the terms: 0.5 + x = -5.389805191 Solving 0.5 + x = -5.389805191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.389805191 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.389805191 + -0.5 x = -5.389805191 + -0.5 Combine like terms: -5.389805191 + -0.5 = -5.889805191 x = -5.889805191 Simplifying x = -5.889805191Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.889805191, -5.889805191}
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