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Simplifying (3x + -15)(2x + -10) = 90 Reorder the terms: (-15 + 3x)(2x + -10) = 90 Reorder the terms: (-15 + 3x)(-10 + 2x) = 90 Multiply (-15 + 3x) * (-10 + 2x) (-15(-10 + 2x) + 3x * (-10 + 2x)) = 90 ((-10 * -15 + 2x * -15) + 3x * (-10 + 2x)) = 90 ((150 + -30x) + 3x * (-10 + 2x)) = 90 (150 + -30x + (-10 * 3x + 2x * 3x)) = 90 (150 + -30x + (-30x + 6x2)) = 90 Combine like terms: -30x + -30x = -60x (150 + -60x + 6x2) = 90 Solving 150 + -60x + 6x2 = 90 Solving for variable 'x'. Reorder the terms: 150 + -90 + -60x + 6x2 = 90 + -90 Combine like terms: 150 + -90 = 60 60 + -60x + 6x2 = 90 + -90 Combine like terms: 90 + -90 = 0 60 + -60x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(10 + -10x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(10 + -10x + x2)' equal to zero and attempt to solve: Simplifying 10 + -10x + x2 = 0 Solving 10 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -10x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -10x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -10x + x2 = 0 + -10 -10x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -10x + x2 = -10 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -10 + 25 Reorder the terms: 25 + -10x + x2 = -10 + 25 Combine like terms: -10 + 25 = 15 25 + -10x + x2 = 15 Factor a perfect square on the left side: (x + -5)(x + -5) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -5) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -5 = 3.872983346 Simplifying x + -5 = 3.872983346 Reorder the terms: -5 + x = 3.872983346 Solving -5 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.872983346 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.872983346 + 5 x = 3.872983346 + 5 Combine like terms: 3.872983346 + 5 = 8.872983346 x = 8.872983346 Simplifying x = 8.872983346Subproblem 2
x + -5 = -3.872983346 Simplifying x + -5 = -3.872983346 Reorder the terms: -5 + x = -3.872983346 Solving -5 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.872983346 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.872983346 + 5 x = -3.872983346 + 5 Combine like terms: -3.872983346 + 5 = 1.127016654 x = 1.127016654 Simplifying x = 1.127016654Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.872983346, 1.127016654}Solution
x = {8.872983346, 1.127016654}
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