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Simplifying 9x2 + 15x + -5 = 2x2 + -10x Reorder the terms: -5 + 15x + 9x2 = 2x2 + -10x Reorder the terms: -5 + 15x + 9x2 = -10x + 2x2 Solving -5 + 15x + 9x2 = -10x + 2x2 Solving for variable 'x'. Reorder the terms: -5 + 15x + 10x + 9x2 + -2x2 = -10x + 2x2 + 10x + -2x2 Combine like terms: 15x + 10x = 25x -5 + 25x + 9x2 + -2x2 = -10x + 2x2 + 10x + -2x2 Combine like terms: 9x2 + -2x2 = 7x2 -5 + 25x + 7x2 = -10x + 2x2 + 10x + -2x2 Reorder the terms: -5 + 25x + 7x2 = -10x + 10x + 2x2 + -2x2 Combine like terms: -10x + 10x = 0 -5 + 25x + 7x2 = 0 + 2x2 + -2x2 -5 + 25x + 7x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5 + 25x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 3.571428571x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 3.571428571x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 3.571428571x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 3.571428571x + x2 = 0 + 0.7142857143 3.571428571x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 3.571428571x + x2 = 0.7142857143 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 = 0.7142857143 + 3.188775511 Reorder the terms: 3.188775511 + 3.571428571x + x2 = 0.7142857143 + 3.188775511 Combine like terms: 0.7142857143 + 3.188775511 = 3.9030612253 3.188775511 + 3.571428571x + x2 = 3.9030612253 Factor a perfect square on the left side: (x + 1.785714286)(x + 1.785714286) = 3.9030612253 Calculate the square root of the right side: 1.97561667 Break this problem into two subproblems by setting (x + 1.785714286) equal to 1.97561667 and -1.97561667.Subproblem 1
x + 1.785714286 = 1.97561667 Simplifying x + 1.785714286 = 1.97561667 Reorder the terms: 1.785714286 + x = 1.97561667 Solving 1.785714286 + x = 1.97561667 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 = 1.97561667 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + x = 1.97561667 + -1.785714286 x = 1.97561667 + -1.785714286 Combine like terms: 1.97561667 + -1.785714286 = 0.189902384 x = 0.189902384 Simplifying x = 0.189902384Subproblem 2
x + 1.785714286 = -1.97561667 Simplifying x + 1.785714286 = -1.97561667 Reorder the terms: 1.785714286 + x = -1.97561667 Solving 1.785714286 + x = -1.97561667 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 = -1.97561667 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + x = -1.97561667 + -1.785714286 x = -1.97561667 + -1.785714286 Combine like terms: -1.97561667 + -1.785714286 = -3.761330956 x = -3.761330956 Simplifying x = -3.761330956Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.189902384, -3.761330956}
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