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Simplifying 8x2 + 16x = 1480 Reorder the terms: 16x + 8x2 = 1480 Solving 16x + 8x2 = 1480 Solving for variable 'x'. Reorder the terms: -1480 + 16x + 8x2 = 1480 + -1480 Combine like terms: 1480 + -1480 = 0 -1480 + 16x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-185 + 2x + x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-185 + 2x + x2)' equal to zero and attempt to solve: Simplifying -185 + 2x + x2 = 0 Solving -185 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '185' to each side of the equation. -185 + 2x + 185 + x2 = 0 + 185 Reorder the terms: -185 + 185 + 2x + x2 = 0 + 185 Combine like terms: -185 + 185 = 0 0 + 2x + x2 = 0 + 185 2x + x2 = 0 + 185 Combine like terms: 0 + 185 = 185 2x + x2 = 185 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 185 + 1 Reorder the terms: 1 + 2x + x2 = 185 + 1 Combine like terms: 185 + 1 = 186 1 + 2x + x2 = 186 Factor a perfect square on the left side: (x + 1)(x + 1) = 186 Calculate the square root of the right side: 13.638181697 Break this problem into two subproblems by setting (x + 1) equal to 13.638181697 and -13.638181697.Subproblem 1
x + 1 = 13.638181697 Simplifying x + 1 = 13.638181697 Reorder the terms: 1 + x = 13.638181697 Solving 1 + x = 13.638181697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 13.638181697 + -1 Combine like terms: 1 + -1 = 0 0 + x = 13.638181697 + -1 x = 13.638181697 + -1 Combine like terms: 13.638181697 + -1 = 12.638181697 x = 12.638181697 Simplifying x = 12.638181697Subproblem 2
x + 1 = -13.638181697 Simplifying x + 1 = -13.638181697 Reorder the terms: 1 + x = -13.638181697 Solving 1 + x = -13.638181697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -13.638181697 + -1 Combine like terms: 1 + -1 = 0 0 + x = -13.638181697 + -1 x = -13.638181697 + -1 Combine like terms: -13.638181697 + -1 = -14.638181697 x = -14.638181697 Simplifying x = -14.638181697Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.638181697, -14.638181697}Solution
x = {12.638181697, -14.638181697}
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