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Simplifying 114 + 8x + x2 + 20x + x = 0 Reorder the terms: 114 + 8x + 20x + x + x2 = 0 Combine like terms: 8x + 20x = 28x 114 + 28x + x + x2 = 0 Combine like terms: 28x + x = 29x 114 + 29x + x2 = 0 Solving 114 + 29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-114' to each side of the equation. 114 + 29x + -114 + x2 = 0 + -114 Reorder the terms: 114 + -114 + 29x + x2 = 0 + -114 Combine like terms: 114 + -114 = 0 0 + 29x + x2 = 0 + -114 29x + x2 = 0 + -114 Combine like terms: 0 + -114 = -114 29x + x2 = -114 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = -114 + 210.25 Reorder the terms: 210.25 + 29x + x2 = -114 + 210.25 Combine like terms: -114 + 210.25 = 96.25 210.25 + 29x + x2 = 96.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + 14.5) equal to 9.810708435 and -9.810708435.Subproblem 1
x + 14.5 = 9.810708435 Simplifying x + 14.5 = 9.810708435 Reorder the terms: 14.5 + x = 9.810708435 Solving 14.5 + x = 9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 9.810708435 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 9.810708435 + -14.5 x = 9.810708435 + -14.5 Combine like terms: 9.810708435 + -14.5 = -4.689291565 x = -4.689291565 Simplifying x = -4.689291565Subproblem 2
x + 14.5 = -9.810708435 Simplifying x + 14.5 = -9.810708435 Reorder the terms: 14.5 + x = -9.810708435 Solving 14.5 + x = -9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -9.810708435 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -9.810708435 + -14.5 x = -9.810708435 + -14.5 Combine like terms: -9.810708435 + -14.5 = -24.310708435 x = -24.310708435 Simplifying x = -24.310708435Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.689291565, -24.310708435}
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