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Simplifying 2x2 + 8 * 5x + -6 = 0 Multiply 8 * 5 2x2 + 40x + -6 = 0 Reorder the terms: -6 + 40x + 2x2 = 0 Solving -6 + 40x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 20x + x2)' equal to zero and attempt to solve: Simplifying -3 + 20x + x2 = 0 Solving -3 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 20x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 20x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 20x + x2 = 0 + 3 20x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 20x + x2 = 3 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 3 + 100 Reorder the terms: 100 + 20x + x2 = 3 + 100 Combine like terms: 3 + 100 = 103 100 + 20x + x2 = 103 Factor a perfect square on the left side: (x + 10)(x + 10) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (x + 10) equal to 10.148891565 and -10.148891565.Subproblem 1
x + 10 = 10.148891565 Simplifying x + 10 = 10.148891565 Reorder the terms: 10 + x = 10.148891565 Solving 10 + x = 10.148891565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 10.148891565 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.148891565 + -10 x = 10.148891565 + -10 Combine like terms: 10.148891565 + -10 = 0.148891565 x = 0.148891565 Simplifying x = 0.148891565Subproblem 2
x + 10 = -10.148891565 Simplifying x + 10 = -10.148891565 Reorder the terms: 10 + x = -10.148891565 Solving 10 + x = -10.148891565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -10.148891565 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.148891565 + -10 x = -10.148891565 + -10 Combine like terms: -10.148891565 + -10 = -20.148891565 x = -20.148891565 Simplifying x = -20.148891565Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.148891565, -20.148891565}Solution
x = {0.148891565, -20.148891565}
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