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Simplifying 2x2 + 12x = 20 Reorder the terms: 12x + 2x2 = 20 Solving 12x + 2x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 12x + 2x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 6x + x2)' equal to zero and attempt to solve: Simplifying -10 + 6x + x2 = 0 Solving -10 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 6x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 6x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 6x + x2 = 0 + 10 6x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 6x + x2 = 10 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 = 10 + 9 Reorder the terms: 9 + 6x + x2 = 10 + 9 Combine like terms: 10 + 9 = 19 9 + 6x + x2 = 19 Factor a perfect square on the left side: (x + 3)(x + 3) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 3) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 3 = 4.358898944 Simplifying x + 3 = 4.358898944 Reorder the terms: 3 + x = 4.358898944 Solving 3 + x = 4.358898944 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 = 4.358898944 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.358898944 + -3 x = 4.358898944 + -3 Combine like terms: 4.358898944 + -3 = 1.358898944 x = 1.358898944 Simplifying x = 1.358898944Subproblem 2
x + 3 = -4.358898944 Simplifying x + 3 = -4.358898944 Reorder the terms: 3 + x = -4.358898944 Solving 3 + x = -4.358898944 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 = -4.358898944 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.358898944 + -3 x = -4.358898944 + -3 Combine like terms: -4.358898944 + -3 = -7.358898944 x = -7.358898944 Simplifying x = -7.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.358898944, -7.358898944}Solution
x = {1.358898944, -7.358898944}
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