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Simplifying 4x2 + 10x + 25 = 9x2 + 18x + 9 Reorder the terms: 25 + 10x + 4x2 = 9x2 + 18x + 9 Reorder the terms: 25 + 10x + 4x2 = 9 + 18x + 9x2 Solving 25 + 10x + 4x2 = 9 + 18x + 9x2 Solving for variable 'x'. Reorder the terms: 25 + -9 + 10x + -18x + 4x2 + -9x2 = 9 + 18x + 9x2 + -9 + -18x + -9x2 Combine like terms: 25 + -9 = 16 16 + 10x + -18x + 4x2 + -9x2 = 9 + 18x + 9x2 + -9 + -18x + -9x2 Combine like terms: 10x + -18x = -8x 16 + -8x + 4x2 + -9x2 = 9 + 18x + 9x2 + -9 + -18x + -9x2 Combine like terms: 4x2 + -9x2 = -5x2 16 + -8x + -5x2 = 9 + 18x + 9x2 + -9 + -18x + -9x2 Reorder the terms: 16 + -8x + -5x2 = 9 + -9 + 18x + -18x + 9x2 + -9x2 Combine like terms: 9 + -9 = 0 16 + -8x + -5x2 = 0 + 18x + -18x + 9x2 + -9x2 16 + -8x + -5x2 = 18x + -18x + 9x2 + -9x2 Combine like terms: 18x + -18x = 0 16 + -8x + -5x2 = 0 + 9x2 + -9x2 16 + -8x + -5x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 16 + -8x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.2 + 1.6x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 1.6x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 1.6x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 1.6x + x2 = 0 + 3.2 1.6x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 1.6x + x2 = 3.2 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 3.2 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 3.2 + 0.64 Combine like terms: 3.2 + 0.64 = 3.84 0.64 + 1.6x + x2 = 3.84 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (x + 0.8) equal to 1.959591794 and -1.959591794.Subproblem 1
x + 0.8 = 1.959591794 Simplifying x + 0.8 = 1.959591794 Reorder the terms: 0.8 + x = 1.959591794 Solving 0.8 + x = 1.959591794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 1.959591794 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.959591794 + -0.8 x = 1.959591794 + -0.8 Combine like terms: 1.959591794 + -0.8 = 1.159591794 x = 1.159591794 Simplifying x = 1.159591794Subproblem 2
x + 0.8 = -1.959591794 Simplifying x + 0.8 = -1.959591794 Reorder the terms: 0.8 + x = -1.959591794 Solving 0.8 + x = -1.959591794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -1.959591794 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.959591794 + -0.8 x = -1.959591794 + -0.8 Combine like terms: -1.959591794 + -0.8 = -2.759591794 x = -2.759591794 Simplifying x = -2.759591794Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.159591794, -2.759591794}
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