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Simplifying -16x2 + 39.2x + -15.6 = 0 Reorder the terms: -15.6 + 39.2x + -16x2 = 0 Solving -15.6 + 39.2x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.975 + -2.45x + x2 = 0 Move the constant term to the right: Add '-0.975' to each side of the equation. 0.975 + -2.45x + -0.975 + x2 = 0 + -0.975 Reorder the terms: 0.975 + -0.975 + -2.45x + x2 = 0 + -0.975 Combine like terms: 0.975 + -0.975 = 0.000 0.000 + -2.45x + x2 = 0 + -0.975 -2.45x + x2 = 0 + -0.975 Combine like terms: 0 + -0.975 = -0.975 -2.45x + x2 = -0.975 The x term is -2.45x. Take half its coefficient (-1.225). Square it (1.500625) and add it to both sides. Add '1.500625' to each side of the equation. -2.45x + 1.500625 + x2 = -0.975 + 1.500625 Reorder the terms: 1.500625 + -2.45x + x2 = -0.975 + 1.500625 Combine like terms: -0.975 + 1.500625 = 0.525625 1.500625 + -2.45x + x2 = 0.525625 Factor a perfect square on the left side: (x + -1.225)(x + -1.225) = 0.525625 Calculate the square root of the right side: 0.725 Break this problem into two subproblems by setting (x + -1.225) equal to 0.725 and -0.725.Subproblem 1
x + -1.225 = 0.725 Simplifying x + -1.225 = 0.725 Reorder the terms: -1.225 + x = 0.725 Solving -1.225 + x = 0.725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.225' to each side of the equation. -1.225 + 1.225 + x = 0.725 + 1.225 Combine like terms: -1.225 + 1.225 = 0.000 0.000 + x = 0.725 + 1.225 x = 0.725 + 1.225 Combine like terms: 0.725 + 1.225 = 1.95 x = 1.95 Simplifying x = 1.95Subproblem 2
x + -1.225 = -0.725 Simplifying x + -1.225 = -0.725 Reorder the terms: -1.225 + x = -0.725 Solving -1.225 + x = -0.725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.225' to each side of the equation. -1.225 + 1.225 + x = -0.725 + 1.225 Combine like terms: -1.225 + 1.225 = 0.000 0.000 + x = -0.725 + 1.225 x = -0.725 + 1.225 Combine like terms: -0.725 + 1.225 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.95, 0.5}
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