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Simplifying 7x2 + 25x + -84 = 0 Reorder the terms: -84 + 25x + 7x2 = 0 Solving -84 + 25x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -12 + 3.571428571x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 3.571428571x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 3.571428571x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 3.571428571x + x2 = 0 + 12 3.571428571x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 3.571428571x + x2 = 12 The x term is 3.571428571x. Take half its coefficient (1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. 3.571428571x + 3.188775511 + x2 = 12 + 3.188775511 Reorder the terms: 3.188775511 + 3.571428571x + x2 = 12 + 3.188775511 Combine like terms: 12 + 3.188775511 = 15.188775511 3.188775511 + 3.571428571x + x2 = 15.188775511 Factor a perfect square on the left side: (x + 1.785714286)(x + 1.785714286) = 15.188775511 Calculate the square root of the right side: 3.897277962 Break this problem into two subproblems by setting (x + 1.785714286) equal to 3.897277962 and -3.897277962.Subproblem 1
x + 1.785714286 = 3.897277962 Simplifying x + 1.785714286 = 3.897277962 Reorder the terms: 1.785714286 + x = 3.897277962 Solving 1.785714286 + x = 3.897277962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.785714286' to each side of the equation. 1.785714286 + -1.785714286 + x = 3.897277962 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + x = 3.897277962 + -1.785714286 x = 3.897277962 + -1.785714286 Combine like terms: 3.897277962 + -1.785714286 = 2.111563676 x = 2.111563676 Simplifying x = 2.111563676Subproblem 2
x + 1.785714286 = -3.897277962 Simplifying x + 1.785714286 = -3.897277962 Reorder the terms: 1.785714286 + x = -3.897277962 Solving 1.785714286 + x = -3.897277962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.785714286' to each side of the equation. 1.785714286 + -1.785714286 + x = -3.897277962 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + x = -3.897277962 + -1.785714286 x = -3.897277962 + -1.785714286 Combine like terms: -3.897277962 + -1.785714286 = -5.682992248 x = -5.682992248 Simplifying x = -5.682992248Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.111563676, -5.682992248}
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