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Simplifying 8x(x + 176) = -72 Reorder the terms: 8x(176 + x) = -72 (176 * 8x + x * 8x) = -72 (1408x + 8x2) = -72 Solving 1408x + 8x2 = -72 Solving for variable 'x'. Reorder the terms: 72 + 1408x + 8x2 = -72 + 72 Combine like terms: -72 + 72 = 0 72 + 1408x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(9 + 176x + x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(9 + 176x + x2)' equal to zero and attempt to solve: Simplifying 9 + 176x + x2 = 0 Solving 9 + 176x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 176x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 176x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 176x + x2 = 0 + -9 176x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 176x + x2 = -9 The x term is 176x. Take half its coefficient (88). Square it (7744) and add it to both sides. Add '7744' to each side of the equation. 176x + 7744 + x2 = -9 + 7744 Reorder the terms: 7744 + 176x + x2 = -9 + 7744 Combine like terms: -9 + 7744 = 7735 7744 + 176x + x2 = 7735 Factor a perfect square on the left side: (x + 88)(x + 88) = 7735 Calculate the square root of the right side: 87.94884877 Break this problem into two subproblems by setting (x + 88) equal to 87.94884877 and -87.94884877.Subproblem 1
x + 88 = 87.94884877 Simplifying x + 88 = 87.94884877 Reorder the terms: 88 + x = 87.94884877 Solving 88 + x = 87.94884877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-88' to each side of the equation. 88 + -88 + x = 87.94884877 + -88 Combine like terms: 88 + -88 = 0 0 + x = 87.94884877 + -88 x = 87.94884877 + -88 Combine like terms: 87.94884877 + -88 = -0.05115123 x = -0.05115123 Simplifying x = -0.05115123Subproblem 2
x + 88 = -87.94884877 Simplifying x + 88 = -87.94884877 Reorder the terms: 88 + x = -87.94884877 Solving 88 + x = -87.94884877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-88' to each side of the equation. 88 + -88 + x = -87.94884877 + -88 Combine like terms: 88 + -88 = 0 0 + x = -87.94884877 + -88 x = -87.94884877 + -88 Combine like terms: -87.94884877 + -88 = -175.94884877 x = -175.94884877 Simplifying x = -175.94884877Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.05115123, -175.94884877}Solution
x = {-0.05115123, -175.94884877}
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