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Simplifying 4x2 + -68x + -280 = 0 Reorder the terms: -280 + -68x + 4x2 = 0 Solving -280 + -68x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-70 + -17x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-70 + -17x + x2)' equal to zero and attempt to solve: Simplifying -70 + -17x + x2 = 0 Solving -70 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -17x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + -17x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -17x + x2 = 0 + 70 -17x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 -17x + x2 = 70 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 70 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 70 + 72.25 Combine like terms: 70 + 72.25 = 142.25 72.25 + -17x + x2 = 142.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (x + -8.5) equal to 11.926860442 and -11.926860442.Subproblem 1
x + -8.5 = 11.926860442 Simplifying x + -8.5 = 11.926860442 Reorder the terms: -8.5 + x = 11.926860442 Solving -8.5 + x = 11.926860442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 11.926860442 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 11.926860442 + 8.5 x = 11.926860442 + 8.5 Combine like terms: 11.926860442 + 8.5 = 20.426860442 x = 20.426860442 Simplifying x = 20.426860442Subproblem 2
x + -8.5 = -11.926860442 Simplifying x + -8.5 = -11.926860442 Reorder the terms: -8.5 + x = -11.926860442 Solving -8.5 + x = -11.926860442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -11.926860442 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -11.926860442 + 8.5 x = -11.926860442 + 8.5 Combine like terms: -11.926860442 + 8.5 = -3.426860442 x = -3.426860442 Simplifying x = -3.426860442Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.426860442, -3.426860442}Solution
x = {20.426860442, -3.426860442}
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