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Simplifying 2x2 + -8x = 152 Reorder the terms: -8x + 2x2 = 152 Solving -8x + 2x2 = 152 Solving for variable 'x'. Reorder the terms: -152 + -8x + 2x2 = 152 + -152 Combine like terms: 152 + -152 = 0 -152 + -8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-76 + -4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-76 + -4x + x2)' equal to zero and attempt to solve: Simplifying -76 + -4x + x2 = 0 Solving -76 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + -4x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + -4x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + -4x + x2 = 0 + 76 -4x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 -4x + x2 = 76 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 = 76 + 4 Reorder the terms: 4 + -4x + x2 = 76 + 4 Combine like terms: 76 + 4 = 80 4 + -4x + x2 = 80 Factor a perfect square on the left side: (x + -2)(x + -2) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -2) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -2 = 8.94427191 Simplifying x + -2 = 8.94427191 Reorder the terms: -2 + x = 8.94427191 Solving -2 + x = 8.94427191 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 = 8.94427191 + 2 Combine like terms: -2 + 2 = 0 0 + x = 8.94427191 + 2 x = 8.94427191 + 2 Combine like terms: 8.94427191 + 2 = 10.94427191 x = 10.94427191 Simplifying x = 10.94427191Subproblem 2
x + -2 = -8.94427191 Simplifying x + -2 = -8.94427191 Reorder the terms: -2 + x = -8.94427191 Solving -2 + x = -8.94427191 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 = -8.94427191 + 2 Combine like terms: -2 + 2 = 0 0 + x = -8.94427191 + 2 x = -8.94427191 + 2 Combine like terms: -8.94427191 + 2 = -6.94427191 x = -6.94427191 Simplifying x = -6.94427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.94427191, -6.94427191}Solution
x = {10.94427191, -6.94427191}
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