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Simplifying 2x2 + 8x + -370 = 0 Reorder the terms: -370 + 8x + 2x2 = 0 Solving -370 + 8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-185 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-185 + 4x + x2)' equal to zero and attempt to solve: Simplifying -185 + 4x + x2 = 0 Solving -185 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '185' to each side of the equation. -185 + 4x + 185 + x2 = 0 + 185 Reorder the terms: -185 + 185 + 4x + x2 = 0 + 185 Combine like terms: -185 + 185 = 0 0 + 4x + x2 = 0 + 185 4x + x2 = 0 + 185 Combine like terms: 0 + 185 = 185 4x + x2 = 185 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 = 185 + 4 Reorder the terms: 4 + 4x + x2 = 185 + 4 Combine like terms: 185 + 4 = 189 4 + 4x + x2 = 189 Factor a perfect square on the left side: (x + 2)(x + 2) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (x + 2) equal to 13.747727085 and -13.747727085.Subproblem 1
x + 2 = 13.747727085 Simplifying x + 2 = 13.747727085 Reorder the terms: 2 + x = 13.747727085 Solving 2 + x = 13.747727085 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 = 13.747727085 + -2 Combine like terms: 2 + -2 = 0 0 + x = 13.747727085 + -2 x = 13.747727085 + -2 Combine like terms: 13.747727085 + -2 = 11.747727085 x = 11.747727085 Simplifying x = 11.747727085Subproblem 2
x + 2 = -13.747727085 Simplifying x + 2 = -13.747727085 Reorder the terms: 2 + x = -13.747727085 Solving 2 + x = -13.747727085 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 = -13.747727085 + -2 Combine like terms: 2 + -2 = 0 0 + x = -13.747727085 + -2 x = -13.747727085 + -2 Combine like terms: -13.747727085 + -2 = -15.747727085 x = -15.747727085 Simplifying x = -15.747727085Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.747727085, -15.747727085}Solution
x = {11.747727085, -15.747727085}
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