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Simplifying 3x2 + 12x + -45 = 0 Reorder the terms: -45 + 12x + 3x2 = 0 Solving -45 + 12x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 4x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-15 + 4x + x2)' equal to zero and attempt to solve: Simplifying -15 + 4x + x2 = 0 Solving -15 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 4x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 4x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4x + x2 = 0 + 15 4x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 4x + x2 = 15 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 15 + 4 Reorder the terms: 4 + 4x + x2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + 4x + x2 = 19 Factor a perfect square on the left side: (x + 2)(x + 2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 2) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 2 = 4.358898944 Simplifying x + 2 = 4.358898944 Reorder the terms: 2 + x = 4.358898944 Solving 2 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.358898944 + -2 x = 4.358898944 + -2 Combine like terms: 4.358898944 + -2 = 2.358898944 x = 2.358898944 Simplifying x = 2.358898944Subproblem 2
x + 2 = -4.358898944 Simplifying x + 2 = -4.358898944 Reorder the terms: 2 + x = -4.358898944 Solving 2 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.358898944 + -2 x = -4.358898944 + -2 Combine like terms: -4.358898944 + -2 = -6.358898944 x = -6.358898944 Simplifying x = -6.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.358898944, -6.358898944}Solution
x = {2.358898944, -6.358898944}
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