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Simplifying 5x2 + 80x + -280 = 35 Reorder the terms: -280 + 80x + 5x2 = 35 Solving -280 + 80x + 5x2 = 35 Solving for variable 'x'. Reorder the terms: -280 + -35 + 80x + 5x2 = 35 + -35 Combine like terms: -280 + -35 = -315 -315 + 80x + 5x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -315 + 80x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-63 + 16x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-63 + 16x + x2)' equal to zero and attempt to solve: Simplifying -63 + 16x + x2 = 0 Solving -63 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 16x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 16x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 16x + x2 = 0 + 63 16x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 16x + x2 = 63 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 63 + 64 Reorder the terms: 64 + 16x + x2 = 63 + 64 Combine like terms: 63 + 64 = 127 64 + 16x + x2 = 127 Factor a perfect square on the left side: (x + 8)(x + 8) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (x + 8) equal to 11.26942767 and -11.26942767.Subproblem 1
x + 8 = 11.26942767 Simplifying x + 8 = 11.26942767 Reorder the terms: 8 + x = 11.26942767 Solving 8 + x = 11.26942767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 11.26942767 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.26942767 + -8 x = 11.26942767 + -8 Combine like terms: 11.26942767 + -8 = 3.26942767 x = 3.26942767 Simplifying x = 3.26942767Subproblem 2
x + 8 = -11.26942767 Simplifying x + 8 = -11.26942767 Reorder the terms: 8 + x = -11.26942767 Solving 8 + x = -11.26942767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -11.26942767 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.26942767 + -8 x = -11.26942767 + -8 Combine like terms: -11.26942767 + -8 = -19.26942767 x = -19.26942767 Simplifying x = -19.26942767Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.26942767, -19.26942767}Solution
x = {3.26942767, -19.26942767}
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