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Simplifying -20x2 + 29x + 5 = 0 Reorder the terms: 5 + 29x + -20x2 = 0 Solving 5 + 29x + -20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -0.25 + -1.45x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.45x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.45x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.45x + x2 = 0 + 0.25 -1.45x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.45x + x2 = 0.25 The x term is -1.45x. Take half its coefficient (-0.725). Square it (0.525625) and add it to both sides. Add '0.525625' to each side of the equation. -1.45x + 0.525625 + x2 = 0.25 + 0.525625 Reorder the terms: 0.525625 + -1.45x + x2 = 0.25 + 0.525625 Combine like terms: 0.25 + 0.525625 = 0.775625 0.525625 + -1.45x + x2 = 0.775625 Factor a perfect square on the left side: (x + -0.725)(x + -0.725) = 0.775625 Calculate the square root of the right side: 0.880695748 Break this problem into two subproblems by setting (x + -0.725) equal to 0.880695748 and -0.880695748.Subproblem 1
x + -0.725 = 0.880695748 Simplifying x + -0.725 = 0.880695748 Reorder the terms: -0.725 + x = 0.880695748 Solving -0.725 + x = 0.880695748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.725' to each side of the equation. -0.725 + 0.725 + x = 0.880695748 + 0.725 Combine like terms: -0.725 + 0.725 = 0.000 0.000 + x = 0.880695748 + 0.725 x = 0.880695748 + 0.725 Combine like terms: 0.880695748 + 0.725 = 1.605695748 x = 1.605695748 Simplifying x = 1.605695748Subproblem 2
x + -0.725 = -0.880695748 Simplifying x + -0.725 = -0.880695748 Reorder the terms: -0.725 + x = -0.880695748 Solving -0.725 + x = -0.880695748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.725' to each side of the equation. -0.725 + 0.725 + x = -0.880695748 + 0.725 Combine like terms: -0.725 + 0.725 = 0.000 0.000 + x = -0.880695748 + 0.725 x = -0.880695748 + 0.725 Combine like terms: -0.880695748 + 0.725 = -0.155695748 x = -0.155695748 Simplifying x = -0.155695748Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.605695748, -0.155695748}
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