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Simplifying (x + -3)(x + -6) = 6x Reorder the terms: (-3 + x)(x + -6) = 6x Reorder the terms: (-3 + x)(-6 + x) = 6x Multiply (-3 + x) * (-6 + x) (-3(-6 + x) + x(-6 + x)) = 6x ((-6 * -3 + x * -3) + x(-6 + x)) = 6x ((18 + -3x) + x(-6 + x)) = 6x (18 + -3x + (-6 * x + x * x)) = 6x (18 + -3x + (-6x + x2)) = 6x Combine like terms: -3x + -6x = -9x (18 + -9x + x2) = 6x Solving 18 + -9x + x2 = 6x Solving for variable 'x'. Reorder the terms: 18 + -9x + -6x + x2 = 6x + -6x Combine like terms: -9x + -6x = -15x 18 + -15x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 18 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -15x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -15x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -15x + x2 = 0 + -18 -15x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -15x + x2 = -18 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -18 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -18 + 56.25 Combine like terms: -18 + 56.25 = 38.25 56.25 + -15x + x2 = 38.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + -7.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + -7.5 = 6.184658438 Simplifying x + -7.5 = 6.184658438 Reorder the terms: -7.5 + x = 6.184658438 Solving -7.5 + x = 6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.184658438 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.184658438 + 7.5 x = 6.184658438 + 7.5 Combine like terms: 6.184658438 + 7.5 = 13.684658438 x = 13.684658438 Simplifying x = 13.684658438Subproblem 2
x + -7.5 = -6.184658438 Simplifying x + -7.5 = -6.184658438 Reorder the terms: -7.5 + x = -6.184658438 Solving -7.5 + x = -6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.184658438 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.184658438 + 7.5 x = -6.184658438 + 7.5 Combine like terms: -6.184658438 + 7.5 = 1.315341562 x = 1.315341562 Simplifying x = 1.315341562Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.684658438, 1.315341562}
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