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Simplifying 47x2 + 21x + -28 = 0 Reorder the terms: -28 + 21x + 47x2 = 0 Solving -28 + 21x + 47x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 47 the coefficient of the squared term: Divide each side by '47'. -0.5957446809 + 0.4468085106x + x2 = 0 Move the constant term to the right: Add '0.5957446809' to each side of the equation. -0.5957446809 + 0.4468085106x + 0.5957446809 + x2 = 0 + 0.5957446809 Reorder the terms: -0.5957446809 + 0.5957446809 + 0.4468085106x + x2 = 0 + 0.5957446809 Combine like terms: -0.5957446809 + 0.5957446809 = 0.0000000000 0.0000000000 + 0.4468085106x + x2 = 0 + 0.5957446809 0.4468085106x + x2 = 0 + 0.5957446809 Combine like terms: 0 + 0.5957446809 = 0.5957446809 0.4468085106x + x2 = 0.5957446809 The x term is 0.4468085106x. Take half its coefficient (0.2234042553). Square it (0.04990946129) and add it to both sides. Add '0.04990946129' to each side of the equation. 0.4468085106x + 0.04990946129 + x2 = 0.5957446809 + 0.04990946129 Reorder the terms: 0.04990946129 + 0.4468085106x + x2 = 0.5957446809 + 0.04990946129 Combine like terms: 0.5957446809 + 0.04990946129 = 0.64565414219 0.04990946129 + 0.4468085106x + x2 = 0.64565414219 Factor a perfect square on the left side: (x + 0.2234042553)(x + 0.2234042553) = 0.64565414219 Calculate the square root of the right side: 0.803526068 Break this problem into two subproblems by setting (x + 0.2234042553) equal to 0.803526068 and -0.803526068.Subproblem 1
x + 0.2234042553 = 0.803526068 Simplifying x + 0.2234042553 = 0.803526068 Reorder the terms: 0.2234042553 + x = 0.803526068 Solving 0.2234042553 + x = 0.803526068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2234042553' to each side of the equation. 0.2234042553 + -0.2234042553 + x = 0.803526068 + -0.2234042553 Combine like terms: 0.2234042553 + -0.2234042553 = 0.0000000000 0.0000000000 + x = 0.803526068 + -0.2234042553 x = 0.803526068 + -0.2234042553 Combine like terms: 0.803526068 + -0.2234042553 = 0.5801218127 x = 0.5801218127 Simplifying x = 0.5801218127Subproblem 2
x + 0.2234042553 = -0.803526068 Simplifying x + 0.2234042553 = -0.803526068 Reorder the terms: 0.2234042553 + x = -0.803526068 Solving 0.2234042553 + x = -0.803526068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2234042553' to each side of the equation. 0.2234042553 + -0.2234042553 + x = -0.803526068 + -0.2234042553 Combine like terms: 0.2234042553 + -0.2234042553 = 0.0000000000 0.0000000000 + x = -0.803526068 + -0.2234042553 x = -0.803526068 + -0.2234042553 Combine like terms: -0.803526068 + -0.2234042553 = -1.0269303233 x = -1.0269303233 Simplifying x = -1.0269303233Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5801218127, -1.0269303233}
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