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Simplifying 90 + (2x)(x + -6) = 180 Remove parenthesis around (2x) 90 + 2x(x + -6) = 180 Reorder the terms: 90 + 2x(-6 + x) = 180 90 + (-6 * 2x + x * 2x) = 180 90 + (-12x + 2x2) = 180 Solving 90 + -12x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 90 + -180 + -12x + 2x2 = 180 + -180 Combine like terms: 90 + -180 = -90 -90 + -12x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -90 + -12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -6x + x2)' equal to zero and attempt to solve: Simplifying -45 + -6x + x2 = 0 Solving -45 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -6x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -6x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -6x + x2 = 0 + 45 -6x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -6x + x2 = 45 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 45 + 9 Reorder the terms: 9 + -6x + x2 = 45 + 9 Combine like terms: 45 + 9 = 54 9 + -6x + x2 = 54 Factor a perfect square on the left side: (x + -3)(x + -3) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + -3) equal to 7.348469228 and -7.348469228.Subproblem 1
x + -3 = 7.348469228 Simplifying x + -3 = 7.348469228 Reorder the terms: -3 + x = 7.348469228 Solving -3 + x = 7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 7.348469228 + 3 Combine like terms: -3 + 3 = 0 0 + x = 7.348469228 + 3 x = 7.348469228 + 3 Combine like terms: 7.348469228 + 3 = 10.348469228 x = 10.348469228 Simplifying x = 10.348469228Subproblem 2
x + -3 = -7.348469228 Simplifying x + -3 = -7.348469228 Reorder the terms: -3 + x = -7.348469228 Solving -3 + x = -7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -7.348469228 + 3 Combine like terms: -3 + 3 = 0 0 + x = -7.348469228 + 3 x = -7.348469228 + 3 Combine like terms: -7.348469228 + 3 = -4.348469228 x = -4.348469228 Simplifying x = -4.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.348469228, -4.348469228}Solution
x = {10.348469228, -4.348469228}
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