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Simplifying (2x + 70)(6x + -30) = 180 Reorder the terms: (70 + 2x)(6x + -30) = 180 Reorder the terms: (70 + 2x)(-30 + 6x) = 180 Multiply (70 + 2x) * (-30 + 6x) (70(-30 + 6x) + 2x * (-30 + 6x)) = 180 ((-30 * 70 + 6x * 70) + 2x * (-30 + 6x)) = 180 ((-2100 + 420x) + 2x * (-30 + 6x)) = 180 (-2100 + 420x + (-30 * 2x + 6x * 2x)) = 180 (-2100 + 420x + (-60x + 12x2)) = 180 Combine like terms: 420x + -60x = 360x (-2100 + 360x + 12x2) = 180 Solving -2100 + 360x + 12x2 = 180 Solving for variable 'x'. Reorder the terms: -2100 + -180 + 360x + 12x2 = 180 + -180 Combine like terms: -2100 + -180 = -2280 -2280 + 360x + 12x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -2280 + 360x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-190 + 30x + x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-190 + 30x + x2)' equal to zero and attempt to solve: Simplifying -190 + 30x + x2 = 0 Solving -190 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '190' to each side of the equation. -190 + 30x + 190 + x2 = 0 + 190 Reorder the terms: -190 + 190 + 30x + x2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + 30x + x2 = 0 + 190 30x + x2 = 0 + 190 Combine like terms: 0 + 190 = 190 30x + x2 = 190 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 190 + 225 Reorder the terms: 225 + 30x + x2 = 190 + 225 Combine like terms: 190 + 225 = 415 225 + 30x + x2 = 415 Factor a perfect square on the left side: (x + 15)(x + 15) = 415 Calculate the square root of the right side: 20.371548787 Break this problem into two subproblems by setting (x + 15) equal to 20.371548787 and -20.371548787.Subproblem 1
x + 15 = 20.371548787 Simplifying x + 15 = 20.371548787 Reorder the terms: 15 + x = 20.371548787 Solving 15 + x = 20.371548787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 20.371548787 + -15 Combine like terms: 15 + -15 = 0 0 + x = 20.371548787 + -15 x = 20.371548787 + -15 Combine like terms: 20.371548787 + -15 = 5.371548787 x = 5.371548787 Simplifying x = 5.371548787Subproblem 2
x + 15 = -20.371548787 Simplifying x + 15 = -20.371548787 Reorder the terms: 15 + x = -20.371548787 Solving 15 + x = -20.371548787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -20.371548787 + -15 Combine like terms: 15 + -15 = 0 0 + x = -20.371548787 + -15 x = -20.371548787 + -15 Combine like terms: -20.371548787 + -15 = -35.371548787 x = -35.371548787 Simplifying x = -35.371548787Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.371548787, -35.371548787}Solution
x = {5.371548787, -35.371548787}
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