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Simplifying 5x2 + 78x + -108 = 0 Reorder the terms: -108 + 78x + 5x2 = 0 Solving -108 + 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'. -21.6 + 15.6x + x2 = 0 Move the constant term to the right: Add '21.6' to each side of the equation. -21.6 + 15.6x + 21.6 + x2 = 0 + 21.6 Reorder the terms: -21.6 + 21.6 + 15.6x + x2 = 0 + 21.6 Combine like terms: -21.6 + 21.6 = 0.0 0.0 + 15.6x + x2 = 0 + 21.6 15.6x + x2 = 0 + 21.6 Combine like terms: 0 + 21.6 = 21.6 15.6x + x2 = 21.6 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 = 21.6 + 60.84 Reorder the terms: 60.84 + 15.6x + x2 = 21.6 + 60.84 Combine like terms: 21.6 + 60.84 = 82.44 60.84 + 15.6x + x2 = 82.44 Factor a perfect square on the left side: (x + 7.8)(x + 7.8) = 82.44 Calculate the square root of the right side: 9.07964757 Break this problem into two subproblems by setting (x + 7.8) equal to 9.07964757 and -9.07964757.Subproblem 1
x + 7.8 = 9.07964757 Simplifying x + 7.8 = 9.07964757 Reorder the terms: 7.8 + x = 9.07964757 Solving 7.8 + x = 9.07964757 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 = 9.07964757 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + x = 9.07964757 + -7.8 x = 9.07964757 + -7.8 Combine like terms: 9.07964757 + -7.8 = 1.27964757 x = 1.27964757 Simplifying x = 1.27964757Subproblem 2
x + 7.8 = -9.07964757 Simplifying x + 7.8 = -9.07964757 Reorder the terms: 7.8 + x = -9.07964757 Solving 7.8 + x = -9.07964757 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 = -9.07964757 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + x = -9.07964757 + -7.8 x = -9.07964757 + -7.8 Combine like terms: -9.07964757 + -7.8 = -16.87964757 x = -16.87964757 Simplifying x = -16.87964757Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.27964757, -16.87964757}
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