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Simplifying (x + -7)(3x) = 120 Reorder the terms: (-7 + x)(3x) = 120 Remove parenthesis around (3x) (-7 + x) * 3x = 120 Reorder the terms for easier multiplication: 3x(-7 + x) = 120 (-7 * 3x + x * 3x) = 120 (-21x + 3x2) = 120 Solving -21x + 3x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + -21x + 3x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + -21x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-40 + -7x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-40 + -7x + x2)' equal to zero and attempt to solve: Simplifying -40 + -7x + x2 = 0 Solving -40 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -7x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -7x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -7x + x2 = 0 + 40 -7x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -7x + x2 = 40 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 40 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 40 + 12.25 Combine like terms: 40 + 12.25 = 52.25 12.25 + -7x + x2 = 52.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + -3.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + -3.5 = 7.228416147 Simplifying x + -3.5 = 7.228416147 Reorder the terms: -3.5 + x = 7.228416147 Solving -3.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 7.228416147 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 7.228416147 + 3.5 x = 7.228416147 + 3.5 Combine like terms: 7.228416147 + 3.5 = 10.728416147 x = 10.728416147 Simplifying x = 10.728416147Subproblem 2
x + -3.5 = -7.228416147 Simplifying x + -3.5 = -7.228416147 Reorder the terms: -3.5 + x = -7.228416147 Solving -3.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -7.228416147 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -7.228416147 + 3.5 x = -7.228416147 + 3.5 Combine like terms: -7.228416147 + 3.5 = -3.728416147 x = -3.728416147 Simplifying x = -3.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.728416147, -3.728416147}Solution
x = {10.728416147, -3.728416147}
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