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Simplifying 20x2 = 29x + -10 Reorder the terms: 20x2 = -10 + 29x Solving 20x2 = -10 + 29x Solving for variable 'x'. Reorder the terms: 10 + -29x + 20x2 = -10 + 29x + 10 + -29x Reorder the terms: 10 + -29x + 20x2 = -10 + 10 + 29x + -29x Combine like terms: -10 + 10 = 0 10 + -29x + 20x2 = 0 + 29x + -29x 10 + -29x + 20x2 = 29x + -29x Combine like terms: 29x + -29x = 0 10 + -29x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.5 + -1.45x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.45x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.45x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.45x + x2 = 0 + -0.5 -1.45x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.45x + x2 = -0.5 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 = -0.5 + 0.525625 Reorder the terms: 0.525625 + -1.45x + x2 = -0.5 + 0.525625 Combine like terms: -0.5 + 0.525625 = 0.025625 0.525625 + -1.45x + x2 = 0.025625 Factor a perfect square on the left side: (x + -0.725)(x + -0.725) = 0.025625 Calculate the square root of the right side: 0.160078106 Break this problem into two subproblems by setting (x + -0.725) equal to 0.160078106 and -0.160078106.Subproblem 1
x + -0.725 = 0.160078106 Simplifying x + -0.725 = 0.160078106 Reorder the terms: -0.725 + x = 0.160078106 Solving -0.725 + x = 0.160078106 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 = 0.160078106 + 0.725 Combine like terms: -0.725 + 0.725 = 0.000 0.000 + x = 0.160078106 + 0.725 x = 0.160078106 + 0.725 Combine like terms: 0.160078106 + 0.725 = 0.885078106 x = 0.885078106 Simplifying x = 0.885078106Subproblem 2
x + -0.725 = -0.160078106 Simplifying x + -0.725 = -0.160078106 Reorder the terms: -0.725 + x = -0.160078106 Solving -0.725 + x = -0.160078106 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 = -0.160078106 + 0.725 Combine like terms: -0.725 + 0.725 = 0.000 0.000 + x = -0.160078106 + 0.725 x = -0.160078106 + 0.725 Combine like terms: -0.160078106 + 0.725 = 0.564921894 x = 0.564921894 Simplifying x = 0.564921894Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.885078106, 0.564921894}
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