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Simplifying 4x2 + -10x + 25 = x2 + 8x + 16 Reorder the terms: 25 + -10x + 4x2 = x2 + 8x + 16 Reorder the terms: 25 + -10x + 4x2 = 16 + 8x + x2 Solving 25 + -10x + 4x2 = 16 + 8x + x2 Solving for variable 'x'. Reorder the terms: 25 + -16 + -10x + -8x + 4x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: 25 + -16 = 9 9 + -10x + -8x + 4x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: -10x + -8x = -18x 9 + -18x + 4x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 9 + -18x + 3x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Reorder the terms: 9 + -18x + 3x2 = 16 + -16 + 8x + -8x + x2 + -1x2 Combine like terms: 16 + -16 = 0 9 + -18x + 3x2 = 0 + 8x + -8x + x2 + -1x2 9 + -18x + 3x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 9 + -18x + 3x2 = 0 + x2 + -1x2 9 + -18x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 9 + -18x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -6x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -6x + x2)' equal to zero and attempt to solve: Simplifying 3 + -6x + x2 = 0 Solving 3 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -6x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6x + x2 = 0 + -3 -6x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6x + x2 = -3 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -3 + 9 Reorder the terms: 9 + -6x + x2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + -6x + x2 = 6 Factor a perfect square on the left side: (x + -3)(x + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -3 = 2.449489743 Simplifying x + -3 = 2.449489743 Reorder the terms: -3 + x = 2.449489743 Solving -3 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.449489743 + 3 x = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 x = 5.449489743 Simplifying x = 5.449489743Subproblem 2
x + -3 = -2.449489743 Simplifying x + -3 = -2.449489743 Reorder the terms: -3 + x = -2.449489743 Solving -3 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.449489743 + 3 x = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 x = 0.550510257 Simplifying x = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.449489743, 0.550510257}Solution
x = {5.449489743, 0.550510257}
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