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Simplifying 5x(x + 12) = 90 Reorder the terms: 5x(12 + x) = 90 (12 * 5x + x * 5x) = 90 (60x + 5x2) = 90 Solving 60x + 5x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 60x + 5x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 60x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-18 + 12x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-18 + 12x + x2)' equal to zero and attempt to solve: Simplifying -18 + 12x + x2 = 0 Solving -18 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 12x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 12x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 12x + x2 = 0 + 18 12x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 12x + x2 = 18 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 18 + 36 Reorder the terms: 36 + 12x + x2 = 18 + 36 Combine like terms: 18 + 36 = 54 36 + 12x + x2 = 54 Factor a perfect square on the left side: (x + 6)(x + 6) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + 6) equal to 7.348469228 and -7.348469228.Subproblem 1
x + 6 = 7.348469228 Simplifying x + 6 = 7.348469228 Reorder the terms: 6 + x = 7.348469228 Solving 6 + x = 7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 7.348469228 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.348469228 + -6 x = 7.348469228 + -6 Combine like terms: 7.348469228 + -6 = 1.348469228 x = 1.348469228 Simplifying x = 1.348469228Subproblem 2
x + 6 = -7.348469228 Simplifying x + 6 = -7.348469228 Reorder the terms: 6 + x = -7.348469228 Solving 6 + x = -7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -7.348469228 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.348469228 + -6 x = -7.348469228 + -6 Combine like terms: -7.348469228 + -6 = -13.348469228 x = -13.348469228 Simplifying x = -13.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.348469228, -13.348469228}Solution
x = {1.348469228, -13.348469228}
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