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Simplifying 5x2 + -29x + -9 = 0 Reorder the terms: -9 + -29x + 5x2 = 0 Solving -9 + -29x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + -5.8x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -5.8x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -5.8x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -5.8x + x2 = 0 + 1.8 -5.8x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -5.8x + x2 = 1.8 The x term is -5.8x. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8x + 8.41 + x2 = 1.8 + 8.41 Reorder the terms: 8.41 + -5.8x + x2 = 1.8 + 8.41 Combine like terms: 1.8 + 8.41 = 10.21 8.41 + -5.8x + x2 = 10.21 Factor a perfect square on the left side: (x + -2.9)(x + -2.9) = 10.21 Calculate the square root of the right side: 3.195309062 Break this problem into two subproblems by setting (x + -2.9) equal to 3.195309062 and -3.195309062.Subproblem 1
x + -2.9 = 3.195309062 Simplifying x + -2.9 = 3.195309062 Reorder the terms: -2.9 + x = 3.195309062 Solving -2.9 + x = 3.195309062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = 3.195309062 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = 3.195309062 + 2.9 x = 3.195309062 + 2.9 Combine like terms: 3.195309062 + 2.9 = 6.095309062 x = 6.095309062 Simplifying x = 6.095309062Subproblem 2
x + -2.9 = -3.195309062 Simplifying x + -2.9 = -3.195309062 Reorder the terms: -2.9 + x = -3.195309062 Solving -2.9 + x = -3.195309062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = -3.195309062 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = -3.195309062 + 2.9 x = -3.195309062 + 2.9 Combine like terms: -3.195309062 + 2.9 = -0.295309062 x = -0.295309062 Simplifying x = -0.295309062Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.095309062, -0.295309062}
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