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Simplifying (4x2 + -6x + 30) + (9x2 + 8x + -82) = 0 Reorder the terms: (30 + -6x + 4x2) + (9x2 + 8x + -82) = 0 Remove parenthesis around (30 + -6x + 4x2) 30 + -6x + 4x2 + (9x2 + 8x + -82) = 0 Reorder the terms: 30 + -6x + 4x2 + (-82 + 8x + 9x2) = 0 Remove parenthesis around (-82 + 8x + 9x2) 30 + -6x + 4x2 + -82 + 8x + 9x2 = 0 Reorder the terms: 30 + -82 + -6x + 8x + 4x2 + 9x2 = 0 Combine like terms: 30 + -82 = -52 -52 + -6x + 8x + 4x2 + 9x2 = 0 Combine like terms: -6x + 8x = 2x -52 + 2x + 4x2 + 9x2 = 0 Combine like terms: 4x2 + 9x2 = 13x2 -52 + 2x + 13x2 = 0 Solving -52 + 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'. -4 + 0.1538461538x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.1538461538x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.1538461538x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.1538461538x + x2 = 0 + 4 0.1538461538x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.1538461538x + x2 = 4 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 = 4 + 0.005917159760 Reorder the terms: 0.005917159760 + 0.1538461538x + x2 = 4 + 0.005917159760 Combine like terms: 4 + 0.005917159760 = 4.00591715976 0.005917159760 + 0.1538461538x + x2 = 4.00591715976 Factor a perfect square on the left side: (x + 0.0769230769)(x + 0.0769230769) = 4.00591715976 Calculate the square root of the right side: 2.001478743 Break this problem into two subproblems by setting (x + 0.0769230769) equal to 2.001478743 and -2.001478743.Subproblem 1
x + 0.0769230769 = 2.001478743 Simplifying x + 0.0769230769 = 2.001478743 Reorder the terms: 0.0769230769 + x = 2.001478743 Solving 0.0769230769 + x = 2.001478743 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 = 2.001478743 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = 2.001478743 + -0.0769230769 x = 2.001478743 + -0.0769230769 Combine like terms: 2.001478743 + -0.0769230769 = 1.9245556661 x = 1.9245556661 Simplifying x = 1.9245556661Subproblem 2
x + 0.0769230769 = -2.001478743 Simplifying x + 0.0769230769 = -2.001478743 Reorder the terms: 0.0769230769 + x = -2.001478743 Solving 0.0769230769 + x = -2.001478743 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 = -2.001478743 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = -2.001478743 + -0.0769230769 x = -2.001478743 + -0.0769230769 Combine like terms: -2.001478743 + -0.0769230769 = -2.0784018199 x = -2.0784018199 Simplifying x = -2.0784018199Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9245556661, -2.0784018199}
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