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Simplifying 2x2 + 4x + -6 = 150 Reorder the terms: -6 + 4x + 2x2 = 150 Solving -6 + 4x + 2x2 = 150 Solving for variable 'x'. Reorder the terms: -6 + -150 + 4x + 2x2 = 150 + -150 Combine like terms: -6 + -150 = -156 -156 + 4x + 2x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -156 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-78 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-78 + 2x + x2)' equal to zero and attempt to solve: Simplifying -78 + 2x + x2 = 0 Solving -78 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + 2x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + 2x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + 2x + x2 = 0 + 78 2x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 2x + x2 = 78 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 78 + 1 Reorder the terms: 1 + 2x + x2 = 78 + 1 Combine like terms: 78 + 1 = 79 1 + 2x + x2 = 79 Factor a perfect square on the left side: (x + 1)(x + 1) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + 1) equal to 8.888194417 and -8.888194417.Subproblem 1
x + 1 = 8.888194417 Simplifying x + 1 = 8.888194417 Reorder the terms: 1 + x = 8.888194417 Solving 1 + x = 8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 8.888194417 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.888194417 + -1 x = 8.888194417 + -1 Combine like terms: 8.888194417 + -1 = 7.888194417 x = 7.888194417 Simplifying x = 7.888194417Subproblem 2
x + 1 = -8.888194417 Simplifying x + 1 = -8.888194417 Reorder the terms: 1 + x = -8.888194417 Solving 1 + x = -8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -8.888194417 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.888194417 + -1 x = -8.888194417 + -1 Combine like terms: -8.888194417 + -1 = -9.888194417 x = -9.888194417 Simplifying x = -9.888194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.888194417, -9.888194417}Solution
x = {7.888194417, -9.888194417}
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