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Simplifying 5x2 + 78x + 143 = 0 Reorder the terms: 143 + 78x + 5x2 = 0 Solving 143 + 78x + 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'. 28.6 + 15.6x + x2 = 0 Move the constant term to the right: Add '-28.6' to each side of the equation. 28.6 + 15.6x + -28.6 + x2 = 0 + -28.6 Reorder the terms: 28.6 + -28.6 + 15.6x + x2 = 0 + -28.6 Combine like terms: 28.6 + -28.6 = 0.0 0.0 + 15.6x + x2 = 0 + -28.6 15.6x + x2 = 0 + -28.6 Combine like terms: 0 + -28.6 = -28.6 15.6x + x2 = -28.6 The x term is 15.6x. Take half its coefficient (7.8). Square it (60.84) and add it to both sides. Add '60.84' to each side of the equation. 15.6x + 60.84 + x2 = -28.6 + 60.84 Reorder the terms: 60.84 + 15.6x + x2 = -28.6 + 60.84 Combine like terms: -28.6 + 60.84 = 32.24 60.84 + 15.6x + x2 = 32.24 Factor a perfect square on the left side: (x + 7.8)(x + 7.8) = 32.24 Calculate the square root of the right side: 5.678027827 Break this problem into two subproblems by setting (x + 7.8) equal to 5.678027827 and -5.678027827.Subproblem 1
x + 7.8 = 5.678027827 Simplifying x + 7.8 = 5.678027827 Reorder the terms: 7.8 + x = 5.678027827 Solving 7.8 + x = 5.678027827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.8' to each side of the equation. 7.8 + -7.8 + x = 5.678027827 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + x = 5.678027827 + -7.8 x = 5.678027827 + -7.8 Combine like terms: 5.678027827 + -7.8 = -2.121972173 x = -2.121972173 Simplifying x = -2.121972173Subproblem 2
x + 7.8 = -5.678027827 Simplifying x + 7.8 = -5.678027827 Reorder the terms: 7.8 + x = -5.678027827 Solving 7.8 + x = -5.678027827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.8' to each side of the equation. 7.8 + -7.8 + x = -5.678027827 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + x = -5.678027827 + -7.8 x = -5.678027827 + -7.8 Combine like terms: -5.678027827 + -7.8 = -13.478027827 x = -13.478027827 Simplifying x = -13.478027827Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.121972173, -13.478027827}
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