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Simplifying 2x2 + -8x + -190 = 0 Reorder the terms: -190 + -8x + 2x2 = 0 Solving -190 + -8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-95 + -4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-95 + -4x + x2)' equal to zero and attempt to solve: Simplifying -95 + -4x + x2 = 0 Solving -95 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + -4x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + -4x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + -4x + x2 = 0 + 95 -4x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 -4x + x2 = 95 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 = 95 + 4 Reorder the terms: 4 + -4x + x2 = 95 + 4 Combine like terms: 95 + 4 = 99 4 + -4x + x2 = 99 Factor a perfect square on the left side: (x + -2)(x + -2) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + -2) equal to 9.949874371 and -9.949874371.Subproblem 1
x + -2 = 9.949874371 Simplifying x + -2 = 9.949874371 Reorder the terms: -2 + x = 9.949874371 Solving -2 + x = 9.949874371 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 = 9.949874371 + 2 Combine like terms: -2 + 2 = 0 0 + x = 9.949874371 + 2 x = 9.949874371 + 2 Combine like terms: 9.949874371 + 2 = 11.949874371 x = 11.949874371 Simplifying x = 11.949874371Subproblem 2
x + -2 = -9.949874371 Simplifying x + -2 = -9.949874371 Reorder the terms: -2 + x = -9.949874371 Solving -2 + x = -9.949874371 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 = -9.949874371 + 2 Combine like terms: -2 + 2 = 0 0 + x = -9.949874371 + 2 x = -9.949874371 + 2 Combine like terms: -9.949874371 + 2 = -7.949874371 x = -7.949874371 Simplifying x = -7.949874371Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.949874371, -7.949874371}Solution
x = {11.949874371, -7.949874371}
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