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Simplifying 3(x + 60)(x + -2) = 60 Reorder the terms: 3(60 + x)(x + -2) = 60 Reorder the terms: 3(60 + x)(-2 + x) = 60 Multiply (60 + x) * (-2 + x) 3(60(-2 + x) + x(-2 + x)) = 60 3((-2 * 60 + x * 60) + x(-2 + x)) = 60 3((-120 + 60x) + x(-2 + x)) = 60 3(-120 + 60x + (-2 * x + x * x)) = 60 3(-120 + 60x + (-2x + x2)) = 60 Combine like terms: 60x + -2x = 58x 3(-120 + 58x + x2) = 60 (-120 * 3 + 58x * 3 + x2 * 3) = 60 (-360 + 174x + 3x2) = 60 Solving -360 + 174x + 3x2 = 60 Solving for variable 'x'. Reorder the terms: -360 + -60 + 174x + 3x2 = 60 + -60 Combine like terms: -360 + -60 = -420 -420 + 174x + 3x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -420 + 174x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-140 + 58x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-140 + 58x + x2)' equal to zero and attempt to solve: Simplifying -140 + 58x + x2 = 0 Solving -140 + 58x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + 58x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 58x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 58x + x2 = 0 + 140 58x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 58x + x2 = 140 The x term is 58x. Take half its coefficient (29). Square it (841) and add it to both sides. Add '841' to each side of the equation. 58x + 841 + x2 = 140 + 841 Reorder the terms: 841 + 58x + x2 = 140 + 841 Combine like terms: 140 + 841 = 981 841 + 58x + x2 = 981 Factor a perfect square on the left side: (x + 29)(x + 29) = 981 Calculate the square root of the right side: 31.320919527 Break this problem into two subproblems by setting (x + 29) equal to 31.320919527 and -31.320919527.Subproblem 1
x + 29 = 31.320919527 Simplifying x + 29 = 31.320919527 Reorder the terms: 29 + x = 31.320919527 Solving 29 + x = 31.320919527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + x = 31.320919527 + -29 Combine like terms: 29 + -29 = 0 0 + x = 31.320919527 + -29 x = 31.320919527 + -29 Combine like terms: 31.320919527 + -29 = 2.320919527 x = 2.320919527 Simplifying x = 2.320919527Subproblem 2
x + 29 = -31.320919527 Simplifying x + 29 = -31.320919527 Reorder the terms: 29 + x = -31.320919527 Solving 29 + x = -31.320919527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + x = -31.320919527 + -29 Combine like terms: 29 + -29 = 0 0 + x = -31.320919527 + -29 x = -31.320919527 + -29 Combine like terms: -31.320919527 + -29 = -60.320919527 x = -60.320919527 Simplifying x = -60.320919527Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.320919527, -60.320919527}Solution
x = {2.320919527, -60.320919527}
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