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Simplifying (x + 3.5)(x + -3.52) = 0 Reorder the terms: (3.5 + x)(x + -3.52) = 0 Reorder the terms: (3.5 + x)(-3.52 + x) = 0 Multiply (3.5 + x) * (-3.52 + x) (3.5(-3.52 + x) + x(-3.52 + x)) = 0 ((-3.52 * 3.5 + x * 3.5) + x(-3.52 + x)) = 0 ((-12.32 + 3.5x) + x(-3.52 + x)) = 0 (-12.32 + 3.5x + (-3.52 * x + x * x)) = 0 (-12.32 + 3.5x + (-3.52x + x2)) = 0 Combine like terms: 3.5x + -3.52x = -0.02x (-12.32 + -0.02x + x2) = 0 Solving -12.32 + -0.02x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12.32' to each side of the equation. -12.32 + -0.02x + 12.32 + x2 = 0 + 12.32 Reorder the terms: -12.32 + 12.32 + -0.02x + x2 = 0 + 12.32 Combine like terms: -12.32 + 12.32 = 0.00 0.00 + -0.02x + x2 = 0 + 12.32 -0.02x + x2 = 0 + 12.32 Combine like terms: 0 + 12.32 = 12.32 -0.02x + x2 = 12.32 The x term is -0.02x. Take half its coefficient (-0.01). Square it (0.0001) and add it to both sides. Add '0.0001' to each side of the equation. -0.02x + 0.0001 + x2 = 12.32 + 0.0001 Reorder the terms: 0.0001 + -0.02x + x2 = 12.32 + 0.0001 Combine like terms: 12.32 + 0.0001 = 12.3201 0.0001 + -0.02x + x2 = 12.3201 Factor a perfect square on the left side: (x + -0.01)(x + -0.01) = 12.3201 Calculate the square root of the right side: 3.51 Break this problem into two subproblems by setting (x + -0.01) equal to 3.51 and -3.51.Subproblem 1
x + -0.01 = 3.51 Simplifying x + -0.01 = 3.51 Reorder the terms: -0.01 + x = 3.51 Solving -0.01 + x = 3.51 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01' to each side of the equation. -0.01 + 0.01 + x = 3.51 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + x = 3.51 + 0.01 x = 3.51 + 0.01 Combine like terms: 3.51 + 0.01 = 3.52 x = 3.52 Simplifying x = 3.52Subproblem 2
x + -0.01 = -3.51 Simplifying x + -0.01 = -3.51 Reorder the terms: -0.01 + x = -3.51 Solving -0.01 + x = -3.51 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01' to each side of the equation. -0.01 + 0.01 + x = -3.51 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + x = -3.51 + 0.01 x = -3.51 + 0.01 Combine like terms: -3.51 + 0.01 = -3.5 x = -3.5 Simplifying x = -3.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.52, -3.5}
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