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Simplifying -16x2 + 17.3x + 2.5 = 1 Reorder the terms: 2.5 + 17.3x + -16x2 = 1 Solving 2.5 + 17.3x + -16x2 = 1 Solving for variable 'x'. Reorder the terms: 2.5 + -1 + 17.3x + -16x2 = 1 + -1 Combine like terms: 2.5 + -1 = 1.5 1.5 + 17.3x + -16x2 = 1 + -1 Combine like terms: 1 + -1 = 0 1.5 + 17.3x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.09375 + -1.08125x + x2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + -1.08125x + 0.09375 + x2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + -1.08125x + x2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + -1.08125x + x2 = 0 + 0.09375 -1.08125x + x2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 -1.08125x + x2 = 0.09375 The x term is -1.08125x. Take half its coefficient (-0.540625). Square it (0.2922753906) and add it to both sides. Add '0.2922753906' to each side of the equation. -1.08125x + 0.2922753906 + x2 = 0.09375 + 0.2922753906 Reorder the terms: 0.2922753906 + -1.08125x + x2 = 0.09375 + 0.2922753906 Combine like terms: 0.09375 + 0.2922753906 = 0.3860253906 0.2922753906 + -1.08125x + x2 = 0.3860253906 Factor a perfect square on the left side: (x + -0.540625)(x + -0.540625) = 0.3860253906 Calculate the square root of the right side: 0.621309416 Break this problem into two subproblems by setting (x + -0.540625) equal to 0.621309416 and -0.621309416.Subproblem 1
x + -0.540625 = 0.621309416 Simplifying x + -0.540625 = 0.621309416 Reorder the terms: -0.540625 + x = 0.621309416 Solving -0.540625 + x = 0.621309416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.540625' to each side of the equation. -0.540625 + 0.540625 + x = 0.621309416 + 0.540625 Combine like terms: -0.540625 + 0.540625 = 0.000000 0.000000 + x = 0.621309416 + 0.540625 x = 0.621309416 + 0.540625 Combine like terms: 0.621309416 + 0.540625 = 1.161934416 x = 1.161934416 Simplifying x = 1.161934416Subproblem 2
x + -0.540625 = -0.621309416 Simplifying x + -0.540625 = -0.621309416 Reorder the terms: -0.540625 + x = -0.621309416 Solving -0.540625 + x = -0.621309416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.540625' to each side of the equation. -0.540625 + 0.540625 + x = -0.621309416 + 0.540625 Combine like terms: -0.540625 + 0.540625 = 0.000000 0.000000 + x = -0.621309416 + 0.540625 x = -0.621309416 + 0.540625 Combine like terms: -0.621309416 + 0.540625 = -0.080684416 x = -0.080684416 Simplifying x = -0.080684416Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.161934416, -0.080684416}
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