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Simplifying 3x2 = 15x + 12 Reorder the terms: 3x2 = 12 + 15x Solving 3x2 = 12 + 15x Solving for variable 'x'. Reorder the terms: -12 + -15x + 3x2 = 12 + 15x + -12 + -15x Reorder the terms: -12 + -15x + 3x2 = 12 + -12 + 15x + -15x Combine like terms: 12 + -12 = 0 -12 + -15x + 3x2 = 0 + 15x + -15x -12 + -15x + 3x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -12 + -15x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + -5x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -5x + x2)' equal to zero and attempt to solve: Simplifying -4 + -5x + x2 = 0 Solving -4 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5x + x2 = 0 + 4 -5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -5x + x2 = 4 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 = 4 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + -5x + x2 = 10.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + -2.5 = 3.201562119 Simplifying x + -2.5 = 3.201562119 Reorder the terms: -2.5 + x = 3.201562119 Solving -2.5 + x = 3.201562119 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 = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.201562119 + 2.5 x = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 x = 5.701562119 Simplifying x = 5.701562119Subproblem 2
x + -2.5 = -3.201562119 Simplifying x + -2.5 = -3.201562119 Reorder the terms: -2.5 + x = -3.201562119 Solving -2.5 + x = -3.201562119 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 = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.201562119 + 2.5 x = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 x = -0.701562119 Simplifying x = -0.701562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.701562119, -0.701562119}Solution
x = {5.701562119, -0.701562119}
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