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Simplifying (x + -4)(x + -9) = 4x Reorder the terms: (-4 + x)(x + -9) = 4x Reorder the terms: (-4 + x)(-9 + x) = 4x Multiply (-4 + x) * (-9 + x) (-4(-9 + x) + x(-9 + x)) = 4x ((-9 * -4 + x * -4) + x(-9 + x)) = 4x ((36 + -4x) + x(-9 + x)) = 4x (36 + -4x + (-9 * x + x * x)) = 4x (36 + -4x + (-9x + x2)) = 4x Combine like terms: -4x + -9x = -13x (36 + -13x + x2) = 4x Solving 36 + -13x + x2 = 4x Solving for variable 'x'. Reorder the terms: 36 + -13x + -4x + x2 = 4x + -4x Combine like terms: -13x + -4x = -17x 36 + -17x + x2 = 4x + -4x Combine like terms: 4x + -4x = 0 36 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -17x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -17x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -17x + x2 = 0 + -36 -17x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -17x + x2 = -36 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -36 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -36 + 72.25 Combine like terms: -36 + 72.25 = 36.25 72.25 + -17x + x2 = 36.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + -8.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + -8.5 = 6.020797289 Simplifying x + -8.5 = 6.020797289 Reorder the terms: -8.5 + x = 6.020797289 Solving -8.5 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 6.020797289 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 6.020797289 + 8.5 x = 6.020797289 + 8.5 Combine like terms: 6.020797289 + 8.5 = 14.520797289 x = 14.520797289 Simplifying x = 14.520797289Subproblem 2
x + -8.5 = -6.020797289 Simplifying x + -8.5 = -6.020797289 Reorder the terms: -8.5 + x = -6.020797289 Solving -8.5 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -6.020797289 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -6.020797289 + 8.5 x = -6.020797289 + 8.5 Combine like terms: -6.020797289 + 8.5 = 2.479202711 x = 2.479202711 Simplifying x = 2.479202711Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.520797289, 2.479202711}
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