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Simplifying 9x2 + -7x + 9 + 4x2 + 9x + -10 = 0 Reorder the terms: 9 + -10 + -7x + 9x + 9x2 + 4x2 = 0 Combine like terms: 9 + -10 = -1 -1 + -7x + 9x + 9x2 + 4x2 = 0 Combine like terms: -7x + 9x = 2x -1 + 2x + 9x2 + 4x2 = 0 Combine like terms: 9x2 + 4x2 = 13x2 -1 + 2x + 13x2 = 0 Solving -1 + 2x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.07692307692 + 0.1538461538x + x2 = 0 Move the constant term to the right: Add '0.07692307692' to each side of the equation. -0.07692307692 + 0.1538461538x + 0.07692307692 + x2 = 0 + 0.07692307692 Reorder the terms: -0.07692307692 + 0.07692307692 + 0.1538461538x + x2 = 0 + 0.07692307692 Combine like terms: -0.07692307692 + 0.07692307692 = 0.00000000000 0.00000000000 + 0.1538461538x + x2 = 0 + 0.07692307692 0.1538461538x + x2 = 0 + 0.07692307692 Combine like terms: 0 + 0.07692307692 = 0.07692307692 0.1538461538x + x2 = 0.07692307692 The x term is 0.1538461538x. Take half its coefficient (0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. 0.1538461538x + 0.005917159760 + x2 = 0.07692307692 + 0.005917159760 Reorder the terms: 0.005917159760 + 0.1538461538x + x2 = 0.07692307692 + 0.005917159760 Combine like terms: 0.07692307692 + 0.005917159760 = 0.08284023668 0.005917159760 + 0.1538461538x + x2 = 0.08284023668 Factor a perfect square on the left side: (x + 0.0769230769)(x + 0.0769230769) = 0.08284023668 Calculate the square root of the right side: 0.287819799 Break this problem into two subproblems by setting (x + 0.0769230769) equal to 0.287819799 and -0.287819799.Subproblem 1
x + 0.0769230769 = 0.287819799 Simplifying x + 0.0769230769 = 0.287819799 Reorder the terms: 0.0769230769 + x = 0.287819799 Solving 0.0769230769 + x = 0.287819799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x = 0.287819799 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = 0.287819799 + -0.0769230769 x = 0.287819799 + -0.0769230769 Combine like terms: 0.287819799 + -0.0769230769 = 0.2108967221 x = 0.2108967221 Simplifying x = 0.2108967221Subproblem 2
x + 0.0769230769 = -0.287819799 Simplifying x + 0.0769230769 = -0.287819799 Reorder the terms: 0.0769230769 + x = -0.287819799 Solving 0.0769230769 + x = -0.287819799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x = -0.287819799 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = -0.287819799 + -0.0769230769 x = -0.287819799 + -0.0769230769 Combine like terms: -0.287819799 + -0.0769230769 = -0.3647428759 x = -0.3647428759 Simplifying x = -0.3647428759Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2108967221, -0.3647428759}
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