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Simplifying 0 = 2x2 + 29x + -5.9 Reorder the terms: 0 = -5.9 + 29x + 2x2 Solving 0 = -5.9 + 29x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 5.9 = 5.9 5.9 + -29x + -2x2 = -5.9 + 29x + 2x2 + 5.9 + -29x + -2x2 Reorder the terms: 5.9 + -29x + -2x2 = -5.9 + 5.9 + 29x + -29x + 2x2 + -2x2 Combine like terms: -5.9 + 5.9 = 0.0 5.9 + -29x + -2x2 = 0.0 + 29x + -29x + 2x2 + -2x2 5.9 + -29x + -2x2 = 29x + -29x + 2x2 + -2x2 Combine like terms: 29x + -29x = 0 5.9 + -29x + -2x2 = 0 + 2x2 + -2x2 5.9 + -29x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 5.9 + -29x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.95 + 14.5x + x2 = 0 Move the constant term to the right: Add '2.95' to each side of the equation. -2.95 + 14.5x + 2.95 + x2 = 0 + 2.95 Reorder the terms: -2.95 + 2.95 + 14.5x + x2 = 0 + 2.95 Combine like terms: -2.95 + 2.95 = 0.00 0.00 + 14.5x + x2 = 0 + 2.95 14.5x + x2 = 0 + 2.95 Combine like terms: 0 + 2.95 = 2.95 14.5x + x2 = 2.95 The x term is 14.5x. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5x + 52.5625 + x2 = 2.95 + 52.5625 Reorder the terms: 52.5625 + 14.5x + x2 = 2.95 + 52.5625 Combine like terms: 2.95 + 52.5625 = 55.5125 52.5625 + 14.5x + x2 = 55.5125 Factor a perfect square on the left side: (x + 7.25)(x + 7.25) = 55.5125 Calculate the square root of the right side: 7.450671111 Break this problem into two subproblems by setting (x + 7.25) equal to 7.450671111 and -7.450671111.Subproblem 1
x + 7.25 = 7.450671111 Simplifying x + 7.25 = 7.450671111 Reorder the terms: 7.25 + x = 7.450671111 Solving 7.25 + x = 7.450671111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = 7.450671111 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 7.450671111 + -7.25 x = 7.450671111 + -7.25 Combine like terms: 7.450671111 + -7.25 = 0.200671111 x = 0.200671111 Simplifying x = 0.200671111Subproblem 2
x + 7.25 = -7.450671111 Simplifying x + 7.25 = -7.450671111 Reorder the terms: 7.25 + x = -7.450671111 Solving 7.25 + x = -7.450671111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = -7.450671111 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -7.450671111 + -7.25 x = -7.450671111 + -7.25 Combine like terms: -7.450671111 + -7.25 = -14.700671111 x = -14.700671111 Simplifying x = -14.700671111Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.200671111, -14.700671111}
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