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Simplifying 15x + 3x2 = 90 Solving 15x + 3x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 15x + 3x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 15x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-30 + 5x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-30 + 5x + x2)' equal to zero and attempt to solve: Simplifying -30 + 5x + x2 = 0 Solving -30 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 5x + x2 = 0 + 30 5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 5x + x2 = 30 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 30 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 30 + 6.25 Combine like terms: 30 + 6.25 = 36.25 6.25 + 5x + x2 = 36.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + 2.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + 2.5 = 6.020797289 Simplifying x + 2.5 = 6.020797289 Reorder the terms: 2.5 + x = 6.020797289 Solving 2.5 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 6.020797289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.020797289 + -2.5 x = 6.020797289 + -2.5 Combine like terms: 6.020797289 + -2.5 = 3.520797289 x = 3.520797289 Simplifying x = 3.520797289Subproblem 2
x + 2.5 = -6.020797289 Simplifying x + 2.5 = -6.020797289 Reorder the terms: 2.5 + x = -6.020797289 Solving 2.5 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -6.020797289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.020797289 + -2.5 x = -6.020797289 + -2.5 Combine like terms: -6.020797289 + -2.5 = -8.520797289 x = -8.520797289 Simplifying x = -8.520797289Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.520797289, -8.520797289}Solution
x = {3.520797289, -8.520797289}
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