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Simplifying 5x2 + 99x + -30 = 0 Reorder the terms: -30 + 99x + 5x2 = 0 Solving -30 + 99x + 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'. -6 + 19.8x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 19.8x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 19.8x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 19.8x + x2 = 0 + 6 19.8x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 19.8x + x2 = 6 The x term is 19.8x. Take half its coefficient (9.9). Square it (98.01) and add it to both sides. Add '98.01' to each side of the equation. 19.8x + 98.01 + x2 = 6 + 98.01 Reorder the terms: 98.01 + 19.8x + x2 = 6 + 98.01 Combine like terms: 6 + 98.01 = 104.01 98.01 + 19.8x + x2 = 104.01 Factor a perfect square on the left side: (x + 9.9)(x + 9.9) = 104.01 Calculate the square root of the right side: 10.198529306 Break this problem into two subproblems by setting (x + 9.9) equal to 10.198529306 and -10.198529306.Subproblem 1
x + 9.9 = 10.198529306 Simplifying x + 9.9 = 10.198529306 Reorder the terms: 9.9 + x = 10.198529306 Solving 9.9 + x = 10.198529306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.9' to each side of the equation. 9.9 + -9.9 + x = 10.198529306 + -9.9 Combine like terms: 9.9 + -9.9 = 0.0 0.0 + x = 10.198529306 + -9.9 x = 10.198529306 + -9.9 Combine like terms: 10.198529306 + -9.9 = 0.298529306 x = 0.298529306 Simplifying x = 0.298529306Subproblem 2
x + 9.9 = -10.198529306 Simplifying x + 9.9 = -10.198529306 Reorder the terms: 9.9 + x = -10.198529306 Solving 9.9 + x = -10.198529306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.9' to each side of the equation. 9.9 + -9.9 + x = -10.198529306 + -9.9 Combine like terms: 9.9 + -9.9 = 0.0 0.0 + x = -10.198529306 + -9.9 x = -10.198529306 + -9.9 Combine like terms: -10.198529306 + -9.9 = -20.098529306 x = -20.098529306 Simplifying x = -20.098529306Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.298529306, -20.098529306}
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