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Simplifying x2 + 9x2 + 30x + 25 = 4x2 + 24x + 36 Reorder the terms: 25 + 30x + x2 + 9x2 = 4x2 + 24x + 36 Combine like terms: x2 + 9x2 = 10x2 25 + 30x + 10x2 = 4x2 + 24x + 36 Reorder the terms: 25 + 30x + 10x2 = 36 + 24x + 4x2 Solving 25 + 30x + 10x2 = 36 + 24x + 4x2 Solving for variable 'x'. Reorder the terms: 25 + -36 + 30x + -24x + 10x2 + -4x2 = 36 + 24x + 4x2 + -36 + -24x + -4x2 Combine like terms: 25 + -36 = -11 -11 + 30x + -24x + 10x2 + -4x2 = 36 + 24x + 4x2 + -36 + -24x + -4x2 Combine like terms: 30x + -24x = 6x -11 + 6x + 10x2 + -4x2 = 36 + 24x + 4x2 + -36 + -24x + -4x2 Combine like terms: 10x2 + -4x2 = 6x2 -11 + 6x + 6x2 = 36 + 24x + 4x2 + -36 + -24x + -4x2 Reorder the terms: -11 + 6x + 6x2 = 36 + -36 + 24x + -24x + 4x2 + -4x2 Combine like terms: 36 + -36 = 0 -11 + 6x + 6x2 = 0 + 24x + -24x + 4x2 + -4x2 -11 + 6x + 6x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 -11 + 6x + 6x2 = 0 + 4x2 + -4x2 -11 + 6x + 6x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -11 + 6x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + x + x2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + x + 1.833333333 + x2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + x + x2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + x + x2 = 0 + 1.833333333 x + x2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 x + x2 = 1.833333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 1.833333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.833333333 + 0.25 Combine like terms: 1.833333333 + 0.25 = 2.083333333 1.25 + x2 = 2.083333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.083333333 Calculate the square root of the right side: 1.443375673 Break this problem into two subproblems by setting (x + 0.5) equal to 1.443375673 and -1.443375673.Subproblem 1
x + 0.5 = 1.443375673 Simplifying x + 0.5 = 1.443375673 Reorder the terms: 0.5 + x = 1.443375673 Solving 0.5 + x = 1.443375673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.443375673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.443375673 + -0.5 x = 1.443375673 + -0.5 Combine like terms: 1.443375673 + -0.5 = 0.943375673 x = 0.943375673 Simplifying x = 0.943375673Subproblem 2
x + 0.5 = -1.443375673 Simplifying x + 0.5 = -1.443375673 Reorder the terms: 0.5 + x = -1.443375673 Solving 0.5 + x = -1.443375673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.443375673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.443375673 + -0.5 x = -1.443375673 + -0.5 Combine like terms: -1.443375673 + -0.5 = -1.943375673 x = -1.943375673 Simplifying x = -1.943375673Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.943375673, -1.943375673}
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